Class 6 Geometry. Answer the questions. For more such worksheets visit (1) If AB and DE are parallel, find the value of ACB.

Size: px
Start display at page:

Download "Class 6 Geometry. Answer the questions. For more such worksheets visit (1) If AB and DE are parallel, find the value of ACB."

Transcription

1 ID : in-6-geometry [1] Class 6 Geometry For more such worksheets visit Answer the questions (1) If AB and DE are parallel, find the value of ACB. (2) If AB and DE are parallel to each other, find the measure of BCD. (3) If lines AC and BD intersects at point O such that AOB: BOC = 2:3, find COD. (4) If AB and PQ are parallel, compute the measure of X.

2 ID : in-6-geometry [2] (5) Find the measure of a+b. (6) If AB and CD are parallel, find the value of angle x. (7) What is the value of the supplement of the complement of 15? (8) If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 1:2, then find the greater of the two angles. (9) Compute the measure of x. (10) If lines XY and MN intersect as shown below and a:b = 2:3, find c.

3 (11) Lines AB and CD intersect at point O. If AOC + BOE = 120 and BOD = 50, find BOE. ID : in-6-geometry [3] (12) If AB and CD are parallel, find the value of x. (13) Find the measure of angle x. (14) If AB and PQ are parallel, compute the measure of W. Check True/False (15) The sum of all the angles around a point is 360. True False

4 ID : in-6-geometry [4] 2017 Edugain ( All Rights Reserved Many more such worksheets can be generated at

5 Answers ID : in-6-geometry [5] (1) 115 In the given figure, BAC = 25 and BDE = 40. According to the question, AB and DE are parallel. Therefore, ABC and BDE are alternate interior angles: ABC = BDE (Alternate interior angles) ABC = 40 The sum of all the three angles of a triangle is 180. Now, in ABC, ABC + BAC + ACB = ACB = 180 (As, ABC = 40 and BAC = 25 ) 65 + ACB = 180 ACB = ACB = 115 Step 4 Therefore, the value of ACB is 115.

6 (2) 48 ID : in-6-geometry [6] Let us extend the line AB to point F such that AF is parallel DE. According to the question, ABC = 114 and CDE = 114. If we look at the given figure carefully, we notice that CGF and CDE are corresponding angles. Therefore, CGF = CDE (Corresponding angles) CGF = 114 (As, CDE = 114 ) Step 4 The angles on a straight line add up to 180. AF is a straight line. So, ABC + CBG = 180 CBG = ABC CBG = (Since, ABC = 114 ) CBG = (1) and also, CGB + CGF = 180 CGB = CGF CGB = CGB = (2) Step 5 The sum of all the three angles of a triangle is 180. Now, in BCG, CBG + BGC + BCG = BCG = 180 (Since, CBG = 66 and BGC = 66 ) BCG = 180 BCG = BCG = 48 Step 6 If we look at the given figure carefully, we notice that BCD = BCG. Therefore, the value of BCD = 48.

7 (3) 72 ID : in-6-geometry [7] Given, AOB: BOC = 2:3, or AOB BOC 3 AOB = 2 BOC AOB = 2 BOC 3 = 2 3, cross multiplying the fractions we get, Since AC is a straight line, we can say that AOB + BOC = 180.Substituting the value of AOB, in the above equation. We have, 2 BOC + BOC = BOC 3 = 180 BOC = = 108. Since AC and BD are straight lines that intersect, COD = BOC = = 72 Step 4 This means that COD = 72

8 (4) 265 ID : in-6-geometry [8] Draw a line MN parallel to both lines AB and PQ. According to the given figure, X1 + X2 + X makes a full angle, i.e., 360. Therefore, X1 + X2 + X = 360 X = X1 - X2 Now, AB and MN are two parallel lines cut by a transversal OB. Hence, NOB = OBA (Alternate angles) X2 = 54 Now, PQ and MN are two parallel lines cut by a transversal OQ. Hence, NOQ = OQP (Alternate angles) X1 = 41 Step 4 We know, X = X1 - X2 = = = 265 Hence, X = 265. (5) 200 If we look at the figure carefully, we notice that the angles b, 160, and a are made around a point. The sum of all the angles around a point is 360. Therefore, b a = 360 a + b = a + b = 200 Hence, the measure of a + b is 200.

9 (6) 120 ID : in-6-geometry [9] It is given that line AB and CD and parallel lines and the third line (say EF) cuts the lines AB and CD at certain angle as shown in the figure above. Let us redraw the figure as below: a = c (vertically opposite angles) c = e (alternate interior angles) Therefore we can write, a = c = e = g Again, b = d (vertically opposite angles) d = f (alternate interior angles) Therefore we can write, b = d = f = h We know that sum of two adjacent angle is equal to 180. Therefore, from the diagram, you can write, a + b = 180, b + c = 180, c + d = 180, d + a = 180 Here, a = 120 and g = x As a is equal to g, x is 120. Therefore, the value of x is 120.

10 (7) 105 ID : in-6-geometry [10] If we look at the question carefully, we notice that we have to find the complement of 15 and then find the supplement of the complement of 15. We know, the sum of the complementary angles is 90. Therefore, the complement of 15, = = 75 The sum of the supplementary angles is 180. Therefore, the supplement of 75, = = 105 Step 4 Hence, the value of the supplement of the complement of 15 is 105. (8) 120 Let x be the first interior angle on the same side of a transversal intersecting two parallel lines. We know that the sum of two interior angles on the same side of a transversal intersecting two parallel lines is 180. Thus, the second interior angle on the same side of a transversal intersecting two parallel lines = x The ratio of the two interior angles on the same side of a transversal intersecting two parallel lines

11 = x x ID : in-6-geometry [11] It is given that the ratio of the two interior angles on the same side of a transversal intersecting two parallel lines = 1:2 x Therefore, = x 2 By cross multiplying, we get: 2x = 1(180 - x) 2x = x 2x + 1x = 180 3x = 180 x = x = 60 Step 4 The first angle = 60 The second angle = = 120 Step 5 Hence, the greater of the two angles is 120. (9) 69 If we look at the angles 113 and (x + 44), we find that they are vertically opposite angles. We know that the vertically opposite angles are equal. Therefore, (x + 44) = 113 x = x = 69

12 (10) 126 ID : in-6-geometry [12] As XY is a straight line, and the sum of the angles on a straight line is equal to 180. We have, a + b + 90 = 180 a + b = 90. We may notice that the angles MOY and XON are vertically opposite angles. So, a + 90 = c (vertically opposite angles are equal). We are given a:b = 2:3, or a b = 2 3. Cross multiplying the fractions, we get, 3a = 2b. Step 4 We put b = 3a 2 in a + b = 90 and get, a + 3a 2 = 90, or 5a 2 = 90, or 5a = 180. Dividing each side by 5, we get, a = 180, or Step 5 Now, since b = 3a 2. We can say that b = , or b = 54. Step 6 From step 2, we have, c = a + 90, or c = , or c = 126.

13 (11) 70 ID : in-6-geometry [13] We are given that BOD = 50. Now, look at the figure. BOD and AOC are vertically opposite angles. So, they are equal. This means, AOC = 50. Since, AOC + BOE = 120. From step 1, we have AOC = 50. We can say that 50 + BOE = 120. Now, subtracting 50 from both the sides, we get, BOE = , or BOE = 70

14 (12) 115 ID : in-6-geometry [14] It is given that lines AB and CD are parallel and the third line (say EF) cuts the lines AB and CD at a certain angle as shown in the figure above. Let us redraw the figure as below: a = c (Vertically opposite angles) c = e (Alternate interior angles) Therefore, we can write, a = c = e = g Again, b = d (Vertically opposite angles) d = f (Alternate interior angles) Therefore, we can write, b = d = f = h We know that sum of two adjacent angles is equal to 180. Therefore, we can write, a + b = 180, b + c = 180, c + d = 180, d + a = 180 Here, h = 115 and d = x As d is equal to h, x is 115. Hence, the value of x is 115.

15 (13) 10 ID : in-6-geometry [15] If we look at the figure carefully, we notice that the angles 160, 13x, and 7x are made around a point. The sum of all the angles around a point is 360. Therefore, x + 7x = x = x = x = 200 x = x = 10 Hence, the measure of angle x is 10.

16 (14) 249 ID : in-6-geometry [16] Draw a line MN parallel to both the line PQ and AB. According to the figure, W = W1 + W2 Now, AB and MN are two parallel lines cut by a transversal OA. Hence, MOA = OAB (Alternate angles) W2 = 54 Now, PQ and MN are two parallel lines cut by a transversal OP. Hence, MOP = OPQ (Alternate angles) W1 = 57 Step 4 We know, W = W1 - W2 = = = 249 (15) True Since, we know that the sum of all the angles around a point must be 360. Therefore, we can say that the statement " The sum of all the angles at a point is 360 " is True.

Class 7 Lines and Angles

Class 7 Lines and Angles ID : in-7-lines-and-angles [1] Class 7 Lines and Angles For more such worksheets visit www.edugain.com Answer the questions (1) ABCD is a quadrilateral whose diagonals intersect each other at point O such

More information

Grade 9 Lines and Angles

Grade 9 Lines and Angles ID : ww-9-lines-and-angles [1] Grade 9 Lines and Angles For more such worksheets visit www.edugain.com Answer t he quest ions (1) If CD is perpendicular to AB, and CE bisect angle ACB, f ind the angle

More information

Grade 7 Lines and Angles

Grade 7 Lines and Angles ID : ww-7-lines-and-angles [1] Grade 7 Lines and Angles For more such worksheets visit www.edugain.com Answer t he quest ions (1) WXYZ is a quadrilateral whose diagonals intersect each other at the point

More information

Grade 9 Lines and Angles

Grade 9 Lines and Angles ID : sg-9-lines-and-angles [1] Grade 9 Lines and Angles For more such worksheets visit www.edugain.com Answer t he quest ions (1) If AB and PQ are parallel, compute the angle Z. (2) Find the value of a+b.

More information

Grade 7 Lines and Angles

Grade 7 Lines and Angles ID : ph-7-lines-and-angles [1] Grade 7 Lines and Angles For more such worksheets visit www.edugain.com Answer t he quest ions (1) If CD is perpendicular to AB, and CE bisect angle ACB, f ind the angle

More information

Grade 7 Lines and Angles

Grade 7 Lines and Angles ID : ae-7-lines-and-angles [1] Grade 7 Lines and Angles For more such worksheets visit www.edugain.com Answer t he quest ions (1) If lines AC and BD intersects at point O such that AOB: BOC = 3:2, f ind

More information

Grade 6 Geometry. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit

Grade 6 Geometry. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit ID : ww-6-geometry [1] Grade 6 Geometry For more such worksheets visit www.edugain.com Answer t he quest ions (1) If AB and CD are parallel, f ind the value of angle x. Choose correct answer(s) f rom given

More information

Class 9 Geometry-Overall

Class 9 Geometry-Overall ID : in-9-geometry-overall [1] Class 9 Geometry-Overall For more such worksheets visit www.edugain.com Answer t he quest ions (1) AB is diameter of the circle. If A and B are connected to E, circle is

More information

Grade 9 Geometry-Overall

Grade 9 Geometry-Overall ID : au-9-geometry-overall [1] Grade 9 Geometry-Overall For more such worksheets visit www.edugain.com Answer t he quest ions (1) A chord of a circle is equal to its radius. Find the angle subtended by

More information

LINES and ANGLES CLASS IX

LINES and ANGLES CLASS IX LINES and ANGLES CLASS IX Questions From CBSE Examination Papers 1. In the given figure, the value of x which makes POQ a straight line is: 6. The complementary angles are in the ratio 1 : 5. Find the

More information

(A) 50 (B) 40 (C) 90 (D) 75. Circles. Circles <1M> 1.It is possible to draw a circle which passes through three collinear points (T/F)

(A) 50 (B) 40 (C) 90 (D) 75. Circles. Circles <1M> 1.It is possible to draw a circle which passes through three collinear points (T/F) Circles 1.It is possible to draw a circle which passes through three collinear points (T/F) 2.The perpendicular bisector of two chords intersect at centre of circle (T/F) 3.If two arcs of a circle

More information

Grade 9 Circles. Answer t he quest ions. For more such worksheets visit

Grade 9 Circles. Answer t he quest ions. For more such worksheets visit ID : th-9-circles [1] Grade 9 Circles For more such worksheets visit www.edugain.com Answer t he quest ions (1) ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it

More information

Grade 9 Circles. Answer the questions. For more such worksheets visit

Grade 9 Circles. Answer the questions. For more such worksheets visit ID : ae-9-circles [1] Grade 9 Circles For more such worksheets visit www.edugain.com Answer the questions (1) Two circles with centres O and O intersect at two points A and B. A line PQ is drawn parallel

More information

Mathematics. Exercise 6.4. (Chapter 6) (Triangles) (Class X) Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2.

Mathematics. Exercise 6.4. (Chapter 6) (Triangles) (Class X) Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2. () Exercise 6.4 Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2. If EF = 15.4 cm, find BC. Answer 1: 1 () Question 2: Diagonals of a trapezium ABCD with AB DC intersect each other

More information

Class 7 Integers. Answer the questions. Choose correct answer(s) from the given choices. Fill in the blanks

Class 7 Integers. Answer the questions. Choose correct answer(s) from the given choices. Fill in the blanks ID : in-7-integers [1] Class 7 Integers For more such worksheets visit www.edugain.com Answer the questions (1) An integer is divided by 4 and gives a remainder of 3. The resulting quotient is divided

More information

6 LINES AND ANGLES EXERCISE 6.1. Q.1. In the figure lines AB and CD intersect at O. If AOC + BOE = 70 and BOD = 40, find BOE and reflex COE.

6 LINES AND ANGLES EXERCISE 6.1. Q.1. In the figure lines AB and CD intersect at O. If AOC + BOE = 70 and BOD = 40, find BOE and reflex COE. 6 LINES AND ANGLES EXERCISE 6.1 Q.1. In the figure lines AB and CD intersect at O. If AOC + BOE = 70 and BOD = 40, find BOE and reflex COE. Sol. Lines AB and CD intersect at O. AOC + BOE = 70 (Given) (1)

More information

Fill in the blanks Chapter 10 Circles Exercise 10.1 Question 1: (i) The centre of a circle lies in of the circle. (exterior/ interior) (ii) A point, whose distance from the centre of a circle is greater

More information

Class 9 Quadrilaterals

Class 9 Quadrilaterals ID : in-9-quadrilaterals [1] Class 9 Quadrilaterals For more such worksheets visit www.edugain.com Answer t he quest ions (1) The diameter of circumcircle of a rectangle is 13 cm and rectangle's width

More information

CLASS IX : CHAPTER - 1 NUMBER SYSTEM

CLASS IX : CHAPTER - 1 NUMBER SYSTEM MCQ WORKSHEET-I CLASS IX : CHAPTER - 1 NUMBER SYSTEM 1. Rational number 3 40 is equal to: (a) 0.75 (b) 0.1 (c) 0.01 (d) 0.075. A rational number between 3 and 4 is: (a) 3 (b) 4 3 (c) 7 (d) 7 4 3. A rational

More information

Properties of the Circle

Properties of the Circle 9 Properties of the Circle TERMINOLOGY Arc: Part of a curve, most commonly a portion of the distance around the circumference of a circle Chord: A straight line joining two points on the circumference

More information

SOLUTIONS SECTION A [1] = 27(27 15)(27 25)(27 14) = 27(12)(2)(13) = cm. = s(s a)(s b)(s c)

SOLUTIONS SECTION A [1] = 27(27 15)(27 25)(27 14) = 27(12)(2)(13) = cm. = s(s a)(s b)(s c) 1. (A) 1 1 1 11 1 + 6 6 5 30 5 5 5 5 6 = 6 6 SOLUTIONS SECTION A. (B) Let the angles be x and 3x respectively x+3x = 180 o (sum of angles on same side of transversal is 180 o ) x=36 0 So, larger angle=3x

More information

Class : IX(CBSE) Worksheet - 1 Sub : Mathematics Topic : Number system

Class : IX(CBSE) Worksheet - 1 Sub : Mathematics Topic : Number system Class : IX(CBSE) Worksheet - Sub : Mathematics Topic : Number system I. Solve the following:. Insert rational numbers between. Epress 57 65 in the decimal form. 8 and.. Epress. as a fraction in the simplest

More information

Class 7 Symmetry. Answer the questions. For more such worksheets visit (1) Find the order of rotational symmetry in the given image.

Class 7 Symmetry. Answer the questions. For more such worksheets visit   (1) Find the order of rotational symmetry in the given image. ID : in-7-symmetry [1] Class 7 Symmetry For more such worksheets visit www.edugain.com Answer the questions (1) Find the order of rotational symmetry in the given image. (2) How many lines of symmetry

More information

Page 1 of 15. Website: Mobile:

Page 1 of 15. Website:    Mobile: Exercise 10.2 Question 1: From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is (A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5

More information

Grade 7 Triangle and its properties

Grade 7 Triangle and its properties ID : ae-7-triangle-and-its-properties [1] Grade 7 Triangle and its properties For more such worksheets visit www.edugain.com Answer t he quest ions (1) In triangle In ΔABC, D is a point on the side BC

More information

Class 8 Factorisation

Class 8 Factorisation ID : in-8-factorisation [1] Class 8 Factorisation For more such worksheets visit www.edugain.com Answer the questions (1) Find factors of following polynomial A) xy - 7y + 9x - 63 B) xy - 5y + 6x - 30

More information

Lesson 13: Angle Sum of a Triangle

Lesson 13: Angle Sum of a Triangle Lesson 13: Angle Sum of a Triangle Classwork Concept Development 1 + 2 + 3 = 4 + 5 + 6 = 7 + 8 + 9 = 180 Note that the sum of angles 7 and 9 must equal 90 because of the known right angle in the right

More information

Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper.

Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper. Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper. 12. What angle has the same measure as its complement? How do you know? 12. What is the

More information

Grade 5 Geometry. Answer the questions. Choose correct answer(s) from the given choices. Fill in the blanks

Grade 5 Geometry. Answer the questions. Choose correct answer(s) from the given choices. Fill in the blanks ID : cn-5-geometry [1] Grade 5 Geometry For more such worksheets visit www.edugain.com Answer the questions (1) What is the common term for the perimeter of a circle? (2) What is the perimeter of an isosceles

More information

Grade 6 Integers. Answer t he quest ions. Fill in the blanks. For more such worksheets visit

Grade 6 Integers. Answer t he quest ions. Fill in the blanks. For more such worksheets visit ID : ae-6-integers [1] Grade 6 Integers For more such worksheets visit www.edugain.com Answer t he quest ions (1) Find the predecessor of each of the f ollowing integers: A) -98 = B) -63 = C) -8 = D) -3

More information

Grade 9 Quadrilaterals

Grade 9 Quadrilaterals ID : ww-9-quadrilaterals [1] Grade 9 Quadrilaterals For more such worksheets visit www.edugain.com Answer t he quest ions (1) ABCD is a rectangle and point P is such that PB = 3 2 cm, PC = 4 cm and PD

More information

Math 9 Chapter 8 Practice Test

Math 9 Chapter 8 Practice Test Name: Class: Date: ID: A Math 9 Chapter 8 Practice Test Short Answer 1. O is the centre of this circle and point Q is a point of tangency. Determine the value of t. If necessary, give your answer to the

More information

10. Circles. Q 5 O is the centre of a circle of radius 5 cm. OP AB and OQ CD, AB CD, AB = 6 cm and CD = 8 cm. Determine PQ. Marks (2) Marks (2)

10. Circles. Q 5 O is the centre of a circle of radius 5 cm. OP AB and OQ CD, AB CD, AB = 6 cm and CD = 8 cm. Determine PQ. Marks (2) Marks (2) 10. Circles Q 1 True or False: It is possible to draw two circles passing through three given non-collinear points. Mark (1) Q 2 State the following statement as true or false. Give reasons also.the perpendicular

More information

16 circles. what goes around...

16 circles. what goes around... 16 circles. what goes around... 2 lesson 16 this is the first of two lessons dealing with circles. this lesson gives some basic definitions and some elementary theorems, the most important of which is

More information

CBSE Sample Paper-05 (Solved) SUMMATIVE ASSESSMENT I MATHEMATICS Class IX. Time allowed: 3 hours Maximum Marks: 90. Section A.

CBSE Sample Paper-05 (Solved) SUMMATIVE ASSESSMENT I MATHEMATICS Class IX. Time allowed: 3 hours Maximum Marks: 90. Section A. CBSE Sample Paper-05 (Solved) SUMMATIVE ASSESSMENT I MATHEMATICS Class IX Time allowed: hours Maximum Marks: 90 General Instructions: a) All questions are compulsory. b) The question paper consists of

More information

21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle.

21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle. 21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle. 22. Prove that If two sides of a cyclic quadrilateral are parallel, then

More information

Class 9 Full Year 9th Grade Review

Class 9 Full Year 9th Grade Review ID : in-9-full-year-9th-grade-review [1] Class 9 Full Year 9th Grade Review For more such worksheets visit www.edugain.com Answer t he quest ions (1) ABCD is a parallelogram with E and F as the mid-points

More information

Grade 9 Full Year 9th Grade Review

Grade 9 Full Year 9th Grade Review ID : ww-9-full-year-9th-grade-review [1] Grade 9 Full Year 9th Grade Review For more such worksheets visit www.edugain.com Answer t he quest ions (1) A carpenter has cut a board in the shape of trapezium.

More information

TRIANGLE EXERCISE 6.4

TRIANGLE EXERCISE 6.4 TRIANGLE EXERCISE 6.4. Let Δ ABC ~ Δ DEF and their areas be, respectively, 64 cm2 and 2 cm2. If EF =5.4 cm, find BC. Ans; According to question ABC~ DEF ar( DEF) = AB2 DE 2 = BC2 EF 2 = AC2 DF 2 64cm 2

More information

Grade 8 Factorisation

Grade 8 Factorisation ID : ae-8-factorisation [1] Grade 8 Factorisation For more such worksheets visit www.edugain.com Answer the questions (1) Find factors of following polynomial A) y 2-2xy + 3y - 6x B) 3y 2-12xy - 2y + 8x

More information

MATHEMATICS CLASS - IX MATHEMATICS CLASS - IX

MATHEMATICS CLASS - IX MATHEMATICS CLASS - IX I, 202 SUMMATIVE SUMMATIVE ASSESSMENT ASSESSMENT I, I, 20 20 SUMMATIVE MATHEMATICS SUMMATIVE ASSESSMENT CLASS - I, IX 202 I, 20 MATHEMATICS CLASS - IX / MATHEMATICS MATHEMATICS CLASS - IX IX / Class IX

More information

Class 8 Multiplication of Polynomials

Class 8 Multiplication of Polynomials ID : in-8-multiplication-of-polynomials [1] Class 8 Multiplication of Polynomials For more such worksheets visit www.edugain.com Answer t he quest ions (1) If (2pq + 2p) ( -2pq + 2p + 2) = ( -4p 2 q 2

More information

Class IX - NCERT Maths Exercise (10.1)

Class IX - NCERT Maths Exercise (10.1) Class IX - NCERT Maths Exercise (10.1) Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/interior) (ii) A point, whose distance from the centre of a circle is greater

More information

POLYNOMIALS ML 5 ZEROS OR ROOTS OF A POLYNOMIAL. A real number α is a root or zero of polynomial f(x) = x + a x + a x +...

POLYNOMIALS ML 5 ZEROS OR ROOTS OF A POLYNOMIAL. A real number α is a root or zero of polynomial f(x) = x + a x + a x +... POLYNOMIALS ML 5 ZEROS OR ROOTS OF A POLYNOMIAL n n 1 n an n 1 n 1 + 0 A real number α is a root or zero of polynomial f(x) = x + a x + a x +... + a x a, n n an n 1 n 1 0 = if f (α) = 0. i.e. α + a + a

More information

Exercise 10.1 Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/ interior)

Exercise 10.1 Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/ interior) Exercise 10.1 Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/ interior) (ii) A point, whose distance from the centre of a circle is greater than its radius lies

More information

Day 31 Bellringer. (a) 2 and 7. (b) 3 and 7. (c) 3 and 6. Page 1

Day 31 Bellringer. (a) 2 and 7. (b) 3 and 7. (c) 3 and 6. Page 1 Day 31 Bellringer 1. In the figure below lines PQ and RS are parallel. State whether the following angles are corresponding, alternate interior or alternate exterior angles. P R 1 2 3 4 5 6 7 8 Q S (a)

More information

Q1. The sum of the lengths of any two sides of a triangle is always (greater/lesser) than the length of the third side. askiitians

Q1. The sum of the lengths of any two sides of a triangle is always (greater/lesser) than the length of the third side. askiitians Class: VII Subject: Math s Topic: Properties of triangle No. of Questions: 20 Q1. The sum of the lengths of any two sides of a triangle is always (greater/lesser) than the length of the third side. Greater

More information

Created by T. Madas 2D VECTORS. Created by T. Madas

Created by T. Madas 2D VECTORS. Created by T. Madas 2D VECTORS Question 1 (**) Relative to a fixed origin O, the point A has coordinates ( 2, 3). The point B is such so that AB = 3i 7j, where i and j are mutually perpendicular unit vectors lying on the

More information

Geometry 3 SIMILARITY & CONGRUENCY Congruency: When two figures have same shape and size, then they are said to be congruent figure. The phenomena between these two figures is said to be congruency. CONDITIONS

More information

Grade 9 Full Year 9th Grade Review

Grade 9 Full Year 9th Grade Review ID : ae-9-full-year-9th-grade-review [1] Grade 9 Full Year 9th Grade Review For more such worksheets visit www.edugain.com Answer t he quest ions (1) The average of Aden's marks in 5 subjects is 79. She

More information

It is known that the length of the tangents drawn from an external point to a circle is equal.

It is known that the length of the tangents drawn from an external point to a circle is equal. CBSE -MATHS-SET 1-2014 Q1. The first three terms of an AP are 3y-1, 3y+5 and 5y+1, respectively. We need to find the value of y. We know that if a, b and c are in AP, then: b a = c b 2b = a + c 2 (3y+5)

More information

9 th CBSE Mega Test - II

9 th CBSE Mega Test - II 9 th CBSE Mega Test - II Time: 3 hours Max. Marks: 90 General Instructions All questions are compulsory. The question paper consists of 34 questions divided into four sections A, B, C and D. Section A

More information

EXERCISE 10.1 EXERCISE 10.2

EXERCISE 10.1 EXERCISE 10.2 NCERT Class 9 Solved Questions for Chapter: Circle 10 NCERT 10 Class CIRCLES 9 Solved Questions for Chapter: Circle EXERCISE 10.1 Q.1. Fill in the blanks : (i) The centre of a circle lies in of the circle.

More information

(5) Find the resultant shape obtained by connecting points (0, 5) (0, 20) (25, 20) and (25, 5).

(5) Find the resultant shape obtained by connecting points (0, 5) (0, 20) (25, 20) and (25, 5). ID : ww-9-olympiad [1] Grade 9 Olympiad For more such worksheets visit www.edugain.com Answer t he quest ions (1) If a cone and hemisphere stands on equal bases, and have the same height. Find the ratio

More information

Grade 6 Integers. Answer t he quest ions. Choose correct answer(s) f rom given choice. Fill in the blanks

Grade 6 Integers. Answer t he quest ions. Choose correct answer(s) f rom given choice. Fill in the blanks ID : ww-6-integers [1] Grade 6 Integers For more such worksheets visit www.edugain.com Answer t he quest ions (1) Subtract : A) -8566 f rom 37583-73166 f rom 13448-62694 f rom 11073 57430 f rom -53545

More information

9. Areas of Parallelograms and Triangles

9. Areas of Parallelograms and Triangles 9. Areas of Parallelograms and Triangles Q 1 State true or false : A diagonal of a parallelogram divides it into two parts of equal areas. Mark (1) Q 2 State true or false: Parallelograms on the same base

More information

ANSWERS. CLASS: VIII TERM - 1 SUBJECT: Mathematics. Exercise: 1(A) Exercise: 1(B)

ANSWERS. CLASS: VIII TERM - 1 SUBJECT: Mathematics. Exercise: 1(A) Exercise: 1(B) ANSWERS CLASS: VIII TERM - 1 SUBJECT: Mathematics TOPIC: 1. Rational Numbers Exercise: 1(A) 1. Fill in the blanks: (i) -21/24 (ii) -4/7 < -4/11 (iii)16/19 (iv)11/13 and -11/13 (v) 0 2. Answer True or False:

More information

Common Core Math 3. Proofs. Can you find the error in this proof "#$%&!!""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""!

Common Core Math 3. Proofs. Can you find the error in this proof #$%&!!! Common Core Math 3 Proofs Can you find the error in this proof "$%& a = b'()$&2 = 1 *+,+$-$%+.. /$,0)%. " a = b $%&'( ) a 2 = ab = a 2 - b 2 = ab - b 2? (a + b)(a - b) = b(a - b) @ (a + b) = b B a + a

More information

Lesson 2B: Thales Theorem

Lesson 2B: Thales Theorem Lesson 2B: Thales Theorem Learning Targets o I can identify radius, diameter, chords, central circles, inscribed circles and semicircles o I can explain that an ABC is a right triangle, then A, B, and

More information

Triangle Congruence and Similarity Review. Show all work for full credit. 5. In the drawing, what is the measure of angle y?

Triangle Congruence and Similarity Review. Show all work for full credit. 5. In the drawing, what is the measure of angle y? Triangle Congruence and Similarity Review Score Name: Date: Show all work for full credit. 1. In a plane, lines that never meet are called. 5. In the drawing, what is the measure of angle y? A. parallel

More information

Grade 7 Integers. Answer the questions. For more such worksheets visit

Grade 7 Integers. Answer the questions. For more such worksheets visit ID : ae-7-integers [1] Grade 7 Integers For more such worksheets visit www.edugain.com Answer the questions (1) A railway company makes a profit of Dhs 1570 on per ticket of business class while loses

More information

2-1 Using Inductive Reasoning to Make Conjectures

2-1 Using Inductive Reasoning to Make Conjectures CHAPTER 2 Chapter Review 2-1 Using Inductive Reasoning to Make Conjectures Find the next term in each pattern. 1. 6, 12, 18,... 2. January, April, July,... 3. The table shows the score on a reaction time

More information

Class IX Chapter 8 Quadrilaterals Maths

Class IX Chapter 8 Quadrilaterals Maths 1 Class IX Chapter 8 Quadrilaterals Maths Exercise 8.1 Question 1: The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral. Let the common ratio between the angles

More information

Class IX Chapter 8 Quadrilaterals Maths

Class IX Chapter 8 Quadrilaterals Maths Class IX Chapter 8 Quadrilaterals Maths Exercise 8.1 Question 1: The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral. Answer: Let the common ratio between

More information

PRMO Solution

PRMO Solution PRMO Solution 0.08.07. How many positive integers less than 000 have the property that the sum of the digits of each such number is divisible by 7 and the number itself is divisible by 3?. Suppose a, b

More information

Class IX Chapter 6 Lines and Angles Maths. Exercise 6.1. In the given figure, lines AB and CD intersect at O. If

Class IX Chapter 6 Lines and Angles Maths. Exercise 6.1. In the given figure, lines AB and CD intersect at O. If Question 1: Exercise 6.1 In the given figure, lines AB and CD intersect at O. If and find BOE and reflex COE. Question 2: In the given figure, lines XY and MN intersect at O. If POY = and a:b = 2 : 3,

More information

Class IX Chapter 6 Lines and Angles Maths

Class IX Chapter 6 Lines and Angles Maths Class IX Chapter 6 Lines and Angles Maths Exercise 6.1 Question 1: In the given figure, lines AB and CD intersect at O. If and find BOE and reflex COE. Question 2: 2 In the given figure, lines XY and MN

More information

The High School Section

The High School Section 1 Viète s Relations The Problems. 1. The equation 10/07/017 The High School Section Session 1 Solutions x 5 11x 4 + 4x 3 + 55x 4x + 175 = 0 has five distinct real roots x 1, x, x 3, x 4, x 5. Find: x 1

More information

0809ge. Geometry Regents Exam Based on the diagram below, which statement is true?

0809ge. Geometry Regents Exam Based on the diagram below, which statement is true? 0809ge 1 Based on the diagram below, which statement is true? 3 In the diagram of ABC below, AB AC. The measure of B is 40. 1) a b ) a c 3) b c 4) d e What is the measure of A? 1) 40 ) 50 3) 70 4) 100

More information

Core Mathematics 2 Radian Measures

Core Mathematics 2 Radian Measures Core Mathematics 2 Radian Measures Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Mathematics 2 Radian Measures 1 Radian Measures Radian measure, including use for arc length and area of sector.

More information

Triangles. 3.In the following fig. AB = AC and BD = DC, then ADC = (A) 60 (B) 120 (C) 90 (D) none 4.In the Fig. given below, find Z.

Triangles. 3.In the following fig. AB = AC and BD = DC, then ADC = (A) 60 (B) 120 (C) 90 (D) none 4.In the Fig. given below, find Z. Triangles 1.Two sides of a triangle are 7 cm and 10 cm. Which of the following length can be the length of the third side? (A) 19 cm. (B) 17 cm. (C) 23 cm. of these. 2.Can 80, 75 and 20 form a triangle?

More information

Geometry 1st semester Exam review game questions

Geometry 1st semester Exam review game questions Class: Date: Geometry 1st semester Exam review game questions Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Name the Property of Equality that justifies

More information

Label carefully each of the following:

Label carefully each of the following: Label carefully each of the following: Circle Geometry labelling activity radius arc diameter centre chord sector major segment tangent circumference minor segment Board of Studies 1 These are the terms

More information

MA 460 Supplement on Analytic Geometry

MA 460 Supplement on Analytic Geometry M 460 Supplement on nalytic Geometry Donu rapura In the 1600 s Descartes introduced cartesian coordinates which changed the way we now do geometry. This also paved for subsequent developments such as calculus.

More information

Class 10 Polynomials. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit

Class 10 Polynomials. Answer t he quest ions. Choose correct answer(s) f rom given choice. For more such worksheets visit ID : in-10-polynomials [1] Class 10 Polynomials For more such worksheets visit www.edugain.com Answer t he quest ions (1) If α and β are the zeros of quadratic polynomial x 2 + px - 2q, f ind the value

More information

Worksheet A VECTORS 1 G H I D E F A B C

Worksheet A VECTORS 1 G H I D E F A B C Worksheet A G H I D E F A B C The diagram shows three sets of equally-spaced parallel lines. Given that AC = p that AD = q, express the following vectors in terms of p q. a CA b AG c AB d DF e HE f AF

More information

2, 10, 30, 68, 130,...

2, 10, 30, 68, 130,... Geometry Unit 4: Reasoning Unit 4 Review Mathematician: Period: Target 1: Discover patterns in a sequence of numbers and figures Directions: Determine what type of is displayed in the given tables. 1)

More information

Class X Chapter 12 Areas Related to Circles Maths

Class X Chapter 12 Areas Related to Circles Maths Exercise 12.1 Question 1: The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles. Radius

More information

Lesson. Warm Up deductive 2. D. 3. I will go to the store; Law of Detachment. Lesson Practice 31

Lesson. Warm Up deductive 2. D. 3. I will go to the store; Law of Detachment. Lesson Practice 31 Warm Up 1. deductive 2. D b. a and b intersect 1 and 2 are supplementary 2 and 3 are supplementary 3. I will go to the store; Law of Detachment Lesson Practice a. 1. 1 and 2 are. 2. 1 and 3 are. 3. m 1

More information

SUMMATIVE ASSESSMENT-1 SAMPLE PAPER (SET-2) MATHEMATICS CLASS IX

SUMMATIVE ASSESSMENT-1 SAMPLE PAPER (SET-2) MATHEMATICS CLASS IX SUMMATIVE ASSESSMENT-1 SAMPLE PAPER (SET-) MATHEMATICS CLASS IX Time: 3 to 3 1 hours Maximum Marks: 80 GENERAL INSTRUCTIONS: 1. All questions are compulsory.. The question paper is divided into four sections

More information

8. Quadrilaterals. If AC = 21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.

8. Quadrilaterals. If AC = 21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ. 8. Quadrilaterals Q 1 Name a quadrilateral whose each pair of opposite sides is equal. Mark (1) Q 2 What is the sum of two consecutive angles in a parallelogram? Mark (1) Q 3 The angles of quadrilateral

More information

= ( +1) BP AC = AP + (1+ )BP Proved UNIT-9 CIRCLES 1. Prove that the parallelogram circumscribing a circle is rhombus. Ans Given : ABCD is a parallelogram circumscribing a circle. To prove : - ABCD is

More information

RMT 2013 Geometry Test Solutions February 2, = 51.

RMT 2013 Geometry Test Solutions February 2, = 51. RMT 0 Geometry Test Solutions February, 0. Answer: 5 Solution: Let m A = x and m B = y. Note that we have two pairs of isosceles triangles, so m A = m ACD and m B = m BCD. Since m ACD + m BCD = m ACB,

More information

GCSE (9-1) Grade 6. Circle Theorems 2

GCSE (9-1) Grade 6. Circle Theorems 2 Name:.. Total Marks: GCSE (9-1) Grade 6 Circle Theorems 2 Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name. Answer all questions. Answer the questions

More information

Sample Question Paper Mathematics First Term (SA - I) Class IX. Time: 3 to 3 ½ hours

Sample Question Paper Mathematics First Term (SA - I) Class IX. Time: 3 to 3 ½ hours Sample Question Paper Mathematics First Term (SA - I) Class IX Time: 3 to 3 ½ hours M.M.:90 General Instructions (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided

More information

Grade 9 Linear Equations in Two Variables

Grade 9 Linear Equations in Two Variables ID : cn-9-linear-equations-in-two-variables [1] Grade 9 Linear Equations in Two Variables For more such worksheets visit www.edugain.com Answer the questions (1) In the graph of the linear equation 4x

More information

UNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 9: Proving Theorems About Triangles Instruction

UNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 9: Proving Theorems About Triangles Instruction Prerequisite Skills This lesson requires the use of the following skills: identifying and using vertical angles, supplementary angles, and complementary angles to find unknown angle measures recognizing

More information

SUMMATIVE ASSESSMENT I, IX / Class IX

SUMMATIVE ASSESSMENT I, IX / Class IX I, 0 SUMMATIVE ASSESSMENT I, 0 0 MATHEMATICS / MATHEMATICS MATHEMATICS CLASS CLASS - IX - IX IX / Class IX MA-0 90 Time allowed : hours Maximum Marks : 90 (i) (ii) 8 6 0 0 (iii) 8 (iv) (v) General Instructions:

More information

Geometry 21 - More Midterm Practice

Geometry 21 - More Midterm Practice Class: Date: Geometry 21 - More Midterm Practice 1. What are the names of three planes that contain point A? 6. If T is the midpoint of SU, what are ST, TU, and SU? A. ST = 7, TU = 63, and SU = 126 B.

More information

PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES

PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES 1. Find the value of k, if x =, y = 1 is a solution of the equation x + 3y = k.. Find the points where the graph of the equation

More information

Definitions, Axioms, Postulates, Propositions, and Theorems from Euclidean and Non-Euclidean Geometries by Marvin Jay Greenberg ( )

Definitions, Axioms, Postulates, Propositions, and Theorems from Euclidean and Non-Euclidean Geometries by Marvin Jay Greenberg ( ) Definitions, Axioms, Postulates, Propositions, and Theorems from Euclidean and Non-Euclidean Geometries by Marvin Jay Greenberg (2009-03-26) Logic Rule 0 No unstated assumptions may be used in a proof.

More information

PLC Papers. Created For:

PLC Papers. Created For: PLC Papers Created For: ed by use of accompanying mark schemes towards the rear to attain 8 out of 10 marks over time by completing Circle Theorems 1 Grade 8 Objective: Apply and prove the standard circle

More information

Udaan School Of Mathematics Class X Chapter 10 Circles Maths

Udaan School Of Mathematics Class X Chapter 10 Circles Maths Exercise 10.1 1. Fill in the blanks (i) The common point of tangent and the circle is called point of contact. (ii) A circle may have two parallel tangents. (iii) A tangent to a circle intersects it in

More information

Important Instructions for the School Principal. (Not to be printed with the question paper)

Important Instructions for the School Principal. (Not to be printed with the question paper) Important Instructions for the School Principal (Not to be printed with the question paper) ) This question paper is strictly meant for use in school based SA-I, September-202 only. This question paper

More information

Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions

Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions Quiz #1. Tuesday, 17 January, 2012. [10 minutes] 1. Given a line segment AB, use (some of) Postulates I V,

More information

2012 GCSE Maths Tutor All Rights Reserved

2012 GCSE Maths Tutor All Rights Reserved 2012 GCSE Maths Tutor All Rights Reserved www.gcsemathstutor.com This book is under copyright to GCSE Maths Tutor. However, it may be distributed freely provided it is not sold for profit. Contents angles

More information

Questions. Exercise (1)

Questions. Exercise (1) Questions Exercise (1) (1) hoose the correct answer: 1) The acute angle supplements. angle. a) acute b) obtuse c) right d) reflex 2) The right angle complements angle whose measure is. a) 0 b) 45 c) 90

More information

1 / 22

1 / 22 CBSE-XII-017 EXAMINATION MATHEMATICS Paper & Solution Time: 3 Hrs. Max. Marks: 90 General Instructions : (i) All questions are compulsory. (ii) The question paper consists of 31 questions divided into

More information

Geometry Honors Review for Midterm Exam

Geometry Honors Review for Midterm Exam Geometry Honors Review for Midterm Exam Format of Midterm Exam: Scantron Sheet: Always/Sometimes/Never and Multiple Choice 40 Questions @ 1 point each = 40 pts. Free Response: Show all work and write answers

More information

Circle Theorems Standard Questions (G10)

Circle Theorems Standard Questions (G10) Circle Theorems Standard Questions (G10) Page 1 Q1.(a) A, B and C are points on the circumference of a circle with centre O. Not drawn accurately Work out the size of angle x. (1) Page 2 (b) P, Q and R

More information