Class 9 Quadrilaterals
|
|
- Kevin Jeremy Tate
- 6 years ago
- Views:
Transcription
1 ID : in-9-quadrilaterals [1] Class 9 Quadrilaterals For more such worksheets visit Answer t he quest ions (1) The diameter of circumcircle of a rectangle is 13 cm and rectangle's width is 5 cm. Find length of the rectangle. (2) In a quadrilateral ABCD, the angles A, B, C and D are in ratio 3:4:5:6. Find the measure of each angle of the quadrilateral. (3) In a parallelogram, prove that the ratio of any side to altitude of adjacent side is same f or all its sides. (4) In a rhombus, one of the diagonals is equal to a side of the rhombus. Find the angles of the rhombus. (5) ABCD is a parallelogram with E and F as the mid-points of side AB and CD. Line segments CE and AF intersect the diagonal BD at point P and Q respectively. If QD = 3 cm and BC = 8 cm, f ind the length of diagonal BD. (6) ABCD is a rectangle and point P is such that PB = 3 2 cm, PC = 4 cm and PD = 3 cm, f ind the value of PA. Choose correct answer(s) f rom given choice (7) ABCD is a parallelogram. L and M are points on AB and DC respectively such that AL = CM. The diagonal BD intersects LM at point O. If AB = 15 cm, AD = 5 cm and LO = 3 cm, f ind the length of OM. a. 7 cm b. 3 cm c. 6 cm d. can not be determined (8) The perimeter of a parallelogram is 180 cm. If one side exceeds the other side by 12 cm, what are the sides of the parallelogram. a. 39 cm, 51 cm b. 41 cm, 53 cm c. 39 cm, 27 cm d. 45 cm, 57 cm
2 ID : in-9-quadrilaterals [2] (9) In a triangle ABC, AD is the median. F is the point on AC such that line BF bisect AD at E. The measure of AC = a. 3AF b. 3AE c. 2AF d. 3EF (10) The length and breadth of a rectangle is 8 cm and 15 cm. Find the radius of circumcircle of this rectangle. a. 8.5 cm b. 17 cm c cm d cm (11) ABCD is a parallelogram and E is the midpoint of side BC. When DE and AB are extended, they meet at point F. If AB = 10 cm and AD = 7 cm, f ind the measure of AF. a. 15 cm b cm c. 30 cm d. 20 cm (12) In a parallelogram ABCD, f ind CDB if DAB = 51 and DBC = 45. a. 84 b. 45 c. 51 d. 39 (13) In the quadrilateral ABCD, AO and DO are the bisectors of A and D respectively. If B = 115 and C = 97 than AOD is: a. 119 b. 96 c. 106 d. 212 (14) ABCD is a quadrilateral and A = B = C = D = 90. Then ABCD can be called as a. Parallelogram b. Square c. Rectangle d. Both rectangle and parallelogram (15) In a parallelogram ABCD, the diagonals bisect at O. What kind of a triangle AOB is? a. a right angled but not an isosceles triangle b. an isosceles but not right angled triangle c. neither isosceles nor a right angled triangle d. an isosceles right angled triangle 2016 Edugain ( All Rights Reserved Many more such worksheets can be generated at
3 Answers ID : in-9-quadrilaterals [3] (1) 12 cm Following f igure shows the rectangle ABCD with it's circumcircle, AB, BC and AC are the length, breadth and diameter of circumcircle of the rectangle ABCD. According to the question, AC = 13 cm, BC = AD = 5 cm. Now, in right angled triangle ABC, AB 2 = AC 2 - BC 2 AB = [ AC 2 - BC 2 ] = [ ] = 12 cm Hence, the length of the rectangle is 12 cm.
4 (2) A = 60, B = 80, C = 100, D = 120 ID : in-9-quadrilaterals [4] Let's assume x is the common f actor of the angles of the quadrilateral. According to the question, the angles A, B, C and D are in ratio 3:4:5:6. Theref ore, A = 3x, B = 4x, C = 5x and D = 6x. We know that the sum of all interior angles of a quadrilateral is equal to 360. Theref ore, A + B + C + D = 360 3x + 4x + 5x + 6x = x = 360 x = x = 20 Hence, A = 3x = 3 20 = 60, B = 4x = 4 20 = 80, C = 5x = 5 20 = 100 and D = 6x = 6 20 = 120.
5 (3) ID : in-9-quadrilaterals [5] Let ABCD is a parallelogram as shown below. We have extended its sides to show the altitudes as CP and CQ Lets f irst consider side AB. Its adjacent sides are AD and BC. From the picture we can see that altitude f or AD and BC is CQ. Theref ore required ratio is, AB CQ Similarly these ratios will be as f ollowing f or other sides CD, AD, BC CQ CP CP Step 4 Theref ore we need to prove that, AB = CD = AD = BC CQ CQ CP CP Step 5 If we compare triangles ΔBPC and ΔDQC, we observe f ollowing, - DQC = BPC... (Both are right angle) - DCQ = BCP... ( DCQ = 90 - BCD and BCP = 90 - BCD) Step 6 Since two angles are equal, triangles ΔBPC and ΔDQC are similar triangles Step 7 Since ratio of corresponding sides of similar triangles is same, BC = CD CP CQ
6 Step 8 ID : in-9-quadrilaterals [6] Also since AB = CD and BC = AD, AB CQ = CD CQ = AD CP = BC CP (4) 60, 120 Following f igure shows the rhombus ABCD, We know that, all sides of a rhombus have equal length. According to the question, the diagonal AC of the rhombus ABCD is equal to the side of the rhombus. Theref ore, AB = BC = CD = DA = AC In ΔABC, AB = BC = CA, Hence, the ΔABC is a equilateral triangle. Step 4 Similarly, the ΔACD is a equilateral triangle. Step 5 All angles of a equilateral triangle is equal to 60. Theref ore, B = D = 60, A = BAC + CAD = = 120, Similarly, the C = 120 Step 6 Hence, the angles of the rhombus are 60 and 120. (5) 9 cm (6) 5 cm (7) b. 3 cm
7 (8) a. 39 cm, 51 cm ID : in-9-quadrilaterals [7] Let's assume a and b are the sides of the parallelogram. The perimeter of the parallelogram = 2(a + b) According to the question, one side of the parallelogram exceeds the other side by 12 cm. Theref ore, a = b + 12 Since, the perimeter of the parallelogram = 180 cm Theref ore, 2(a + b) = 180 2(b b) = 180 (2b + 12) = 180/2 2b = b = 78 2 b = 39 cm, a = b + 12 = = 51 cm Step 4 Hence, the sides of the parallelogram are 39 cm and 51 cm.
8 (9) a. 3AF ID : in-9-quadrilaterals [8] Following picture shows triangle ΔABC with median AD at E, and another line BF, which bisects AD. We have also drawn another line DG which is parallel to BF From proportionality theorem we know that if a line is drawn parallel to one side of a triangle, it divides other two sides in the same ration For triangle ΔBFC, DG is parallel to BF and using proportionality theorem we can f ind that, FG = BD GC DC Step 4 Since we know that BD = DC, we can f ind that GC = FG... (1) Step 5 Similarly we can use proportionality theorem f or triangle ΔADG, AF = AE FG ED Step 6 But since AE = ED, FG = AF... (2) Step 7 Theref ore, AC = AF + FG + GC Using relation (1) and (2), AC = AF + AF + AF, AC = 3 AF
9 (10) a. 8.5 cm ID : in-9-quadrilaterals [9] Following f igure shows the rectangle ABCD with it's circumcircle, AB, BC and AC are the length, breadth and diameter of circumcircle of the rectangle ABCD. According to the question, AB = 15 cm, BC = 8 cm. Now, in right angled triangle ABC, AC 2 = AB 2 + BC 2 AC = [ AB 2 + BC 2 ] = [ ] = 17 cm The diameter of circumcircle of the rectangle = 17 cm. The radius of circumcircle of the rectangle = 17/2 = 8.5 cm. (11) d. 20 cm
10 (12) a. 84 ID : in-9-quadrilaterals [10] Following f igure shows the parallelogram ABCD, According to the question DAB = 51 and DBC = 45. A = C = 51 [Since the opposite angles of a parallelogram are congruent.] In ΔBCD, DBC + BCD + CDB = 180 [Since the sum of all the angles of a triangle is 180 ] CDB = CDB = 180 CDB = CDB = 84 Hence, the value of the CDB is 84.
11 (13) c. 106 ID : in-9-quadrilaterals [11] Following f igure shows the quadrilateral ABCD, According to the question, AO and DO are the bisectors of A and D respectively. Theref ore, DAO = A/2, ADO = D/2, B = 115, C = 97 We know that the sum of all angles of a quadrilateral is equals to 360. Theref ore, A + B + C + D = 360 A D = 360 A + D = 360 A + D = A + D = (1) In ΔAOD, DAO + ADO + AOD = [Since, we know that the sum of all three angles of a triangle is equals to 180 ] A/2 + D/2 + AOD = 180 AOD = A/2 - D/ A - D AOD = 2 AOD = ( A + D) AOD = 2 AOD = [From equation (1)] Step 4 Hence, the value of AOD is 106.
12 (14) d. Both rectangle and parallelogram ID : in-9-quadrilaterals [12] Following f igure shows the quadrilateral ABCD where all f our angles are 90 A quadrilateral with all f our angles of 90 is a rectangle. We also know that all rectangles are parallelogram since opposite sides of rectangles are parallel and equal to each other. T heref ore, the correct answer is 'Both rectangle and parallelogram'. (15) c. neither isosceles nor a right angled triangle Following f igure shows the parallelogram ABCD with diagonals. We know that diagonals of a parallelogram bisects each other but they are not perpendicular, theref ore AOC 90, and AO = AC/2 and OB = BD/2 Also since diagonals of parallelogram are not equal, AC BD AC/2 BD/2 AO OB Step 4 Since AO OB and AOC 90, triangle ΔAOB is neither isosceles nor a right angled triangle.
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 informationGrade 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 informationGrade 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 informationGrade 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 informationGrade 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 informationGrade 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 informationGrade 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 informationGrade 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 information8. 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 informationDownloaded from
Triangles 1.In ABC right angled at C, AD is median. Then AB 2 = AC 2 - AD 2 AD 2 - AC 2 3AC 2-4AD 2 (D) 4AD 2-3AC 2 2.Which of the following statement is true? Any two right triangles are similar
More informationGrade 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 informationClass 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(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 informationTRIANGLES CHAPTER 7. (A) Main Concepts and Results. (B) Multiple Choice Questions
CHAPTER 7 TRIANGLES (A) Main Concepts and Results Triangles and their parts, Congruence of triangles, Congruence and correspondence of vertices, Criteria for Congruence of triangles: (i) SAS (ii) ASA (iii)
More informationGrade 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 information21. 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 informationGrade 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 informationClass 7 Mensuration - Perimeter, Area, Volume
ID : U-92206-76-2397-Mensuration-Perimeter-Area-Volume [1] Class 7 Mensuration - Perimeter, Area, Volume For more such worksheets visit www.edugain.com Answer t he quest ions (1) The cost of f encing is
More information0114ge. Geometry Regents Exam 0114
0114ge 1 The midpoint of AB is M(4, 2). If the coordinates of A are (6, 4), what are the coordinates of B? 1) (1, 3) 2) (2, 8) 3) (5, 1) 4) (14, 0) 2 Which diagram shows the construction of a 45 angle?
More informationVisit: ImperialStudy.com For More Study Materials Class IX Chapter 12 Heron s Formula Maths
Exercise 1.1 1. Find the area of a triangle whose sides are respectively 150 cm, 10 cm and 00 cm. The triangle whose sides are a = 150 cm b = 10 cm c = 00 cm The area of a triangle = s(s a)(s b)(s c) Here
More informationClass 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 informationNozha Directorate of Education Form : 2 nd Prep
Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep Nozha Language Schools Geometry Revision Sheet Ismailia Road Branch Sheet ( 1) 1-Complete 1. In the parallelogram, each
More informationGrade 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 informationSOLUTIONS 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 informationNozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Ismailia Road Branch
Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch Sheet ( 1) 1-Complete 1. in the parallelogram, each two opposite
More information0809ge. 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 informationPRACTICE 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 information10. 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 informationTriangles. 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 informationGeometry 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 informationChapter (Circle) * Circle - circle is locus of such points which are at equidistant from a fixed point in
Chapter - 10 (Circle) Key Concept * Circle - circle is locus of such points which are at equidistant from a fixed point in a plane. * Concentric circle - Circle having same centre called concentric circle.
More informationClass 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 informationClass 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( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear.
Problems 01 - POINT Page 1 ( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear. ( ) Prove that the two lines joining the mid-points of the pairs of opposite sides and the line
More informationAREAS OF PARALLELOGRAMS AND TRIANGLES
AREAS OF PARALLELOGRAMS AND TRIANGLES Main Concepts and Results: The area of a closed plane figure is the measure of the region inside the figure: Fig.1 The shaded parts (Fig.1) represent the regions whose
More information0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below.
0611ge 1 Line segment AB is shown in the diagram below. In the diagram below, A B C is a transformation of ABC, and A B C is a transformation of A B C. Which two sets of construction marks, labeled I,
More informationGrade 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 information0113ge. Geometry Regents Exam In the diagram below, under which transformation is A B C the image of ABC?
0113ge 1 If MNP VWX and PM is the shortest side of MNP, what is the shortest side of VWX? 1) XV ) WX 3) VW 4) NP 4 In the diagram below, under which transformation is A B C the image of ABC? In circle
More information6 CHAPTER. Triangles. A plane figure bounded by three line segments is called a triangle.
6 CHAPTER We are Starting from a Point but want to Make it a Circle of Infinite Radius A plane figure bounded by three line segments is called a triangle We denote a triangle by the symbol In fig ABC has
More information1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle?
1 For all problems, NOTA stands for None of the Above. 1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle? (A) 40 (B) 60 (C) 80 (D) Cannot be determined
More informationchapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?
chapter vector geometry solutions V. Exercise A. For the shape shown, find a single vector which is equal to a)!!! " AB + BC AC b)! AD!!! " + DB AB c)! AC + CD AD d)! BC + CD!!! " + DA BA e) CD!!! " "
More informationMathematics 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 information9. 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 informationClass 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 informationTHEOREMS WE KNOW PROJECT
1 This is a list of all of the theorems that you know and that will be helpful when working on proofs for the rest of the unit. In the Notes section I would like you to write anything that will help you
More informationRMT 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 informationRhombi, Rectangles and Squares
Rhombi, Rectangles and Squares Math Practice Return to the Table of Contents 1 Three Special Parallelograms All the same properties of a parallelogram apply to the rhombus, rectangle, and square. Rhombus
More information1) Exercise 1 In the diagram, ABC = AED, AD = 3, DB = 2 and AE = 2. Determine the length of EC. Solution:
1) Exercise 1 In the diagram, ABC = AED, AD = 3, DB = 2 and AE = 2. Determine the length of EC. Solution: First, we show that AED and ABC are similar. Since DAE = BAC and ABC = AED, we have that AED is
More informationMath 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 informationVAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER)
BY:Prof. RAHUL MISHRA Class :- X QNo. VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) CIRCLES Subject :- Maths General Instructions Questions M:9999907099,9818932244 1 In the adjoining figures, PQ
More information1 st Preparatory. Part (1)
Part (1) (1) omplete: 1) The square is a rectangle in which. 2) in a parallelogram in which m ( ) = 60, then m ( ) =. 3) The sum of measures of the angles of the quadrilateral equals. 4) The ray drawn
More informationCHAPTER 7 TRIANGLES. 7.1 Introduction. 7.2 Congruence of Triangles
CHAPTER 7 TRIANGLES 7.1 Introduction You have studied about triangles and their various properties in your earlier classes. You know that a closed figure formed by three intersecting lines is called a
More information0610ge. Geometry Regents Exam The diagram below shows a right pentagonal prism.
0610ge 1 In the diagram below of circle O, chord AB chord CD, and chord CD chord EF. 3 The diagram below shows a right pentagonal prism. Which statement must be true? 1) CE DF 2) AC DF 3) AC CE 4) EF CD
More informationKENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION
KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 02 F PERIODIC TEST III EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS IX Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks)
More information9 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 informationPart (1) Second : Trigonometry. Tan
Part (1) Second : Trigonometry (1) Complete the following table : The angle Ratio 42 12 \ Sin 0.3214 Cas 0.5321 Tan 2.0625 (2) Complete the following : 1) 46 36 \ 24 \\ =. In degrees. 2) 44.125 = in degrees,
More informationExercise 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 informationUNIT-8 SIMILAR TRIANGLES Geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for art. 1. ABC is a right-angled triangle, right-angled
More information0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 2) 8 3) 3 4) 6 2 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
More informationFill 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 informationEXERCISE 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 informationClass 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 informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, January 27, 2011 9:15 a.m. to 12:15 p.m., only Student Name: School Name: Print your name and the name
More information1 What is the solution of the system of equations graphed below? y = 2x + 1
1 What is the solution of the system of equations graphed below? y = 2x + 1 3 As shown in the diagram below, when hexagon ABCDEF is reflected over line m, the image is hexagon A'B'C'D'E'F'. y = x 2 + 2x
More information0612ge. Geometry Regents Exam
0612ge 1 Triangle ABC is graphed on the set of axes below. 3 As shown in the diagram below, EF intersects planes P, Q, and R. Which transformation produces an image that is similar to, but not congruent
More informationSOLUTION. Taken together, the preceding equations imply that ABC DEF by the SSS criterion for triangle congruence.
1. [20 points] Suppose that we have ABC and DEF in the Euclidean plane and points G and H on (BC) and (EF) respectively such that ABG DEH and AGC DHF. Prove that ABC DEF. The first congruence assumption
More informationLLT Education Services
8. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle. (a) 4 cm (b) 3 cm (c) 6 cm (d) 5 cm 9. From a point P, 10 cm away from 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)
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(b) the equation of the perpendicular bisector of AB. [3]
HORIZON EDUCATION SINGAPORE Additional Mathematics Practice Questions: Coordinate Geometr 1 Set 1 1 In the figure, ABCD is a rhombus with coordinates A(2, 9) and C(8, 1). The diagonals AC and BD cut at
More informationName: Class: Date: c. WZ XY and XW YZ. b. WZ ZY and XW YZ. d. WN NZ and YN NX
Class: Date: 2nd Semester Exam Review - Geometry CP 1. Complete this statement: A polygon with all sides the same length is said to be. a. regular b. equilateral c. equiangular d. convex 3. Which statement
More information0811ge. Geometry Regents Exam
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 ) 8 3) 3 4) 6 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
More informationTriangles. Chapter Flowchart. The Chapter Flowcharts give you the gist of the chapter flow in a single glance.
Triangles Chapter Flowchart The Chapter Flowcharts give you the gist of the chapter flow in a single glance. Triangle A plane figure bounded by three line segments is called a triangle. Types of Triangles
More informationLos Angeles Unified School District Periodic Assessments. Geometry. Assessment 2 ASSESSMENT CODE LA08_G_T2_TST_31241
Los Angeles Unified School District Periodic Assessments Assessment 2 2008 2009 Los Angeles Unified School District Periodic Assessments LA08_G_T2_TST_31241 ASSESSMENT ODE 1100209 The test items contained
More informationCBSE Sample Paper-03 (Unsolved) SUMMATIVE ASSESSMENT II MATHEMATICS Class IX. Time allowed: 3 hours Maximum Marks: 90
CBSE Sample Paper-3 (Unsolved) SUMMATIVE ASSESSMENT II MATHEMATICS Class IX Time allowed: 3 hours Maximum Marks: 9 General Instructions: a) All questions are compulsory. b) The question paper consists
More informationClass 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[BIT Ranchi 1992] (a) 2 (b) 3 (c) 4 (d) 5. (d) None of these. then the direction cosine of AB along y-axis is [MNR 1989]
VECTOR ALGEBRA o. Let a i be a vector which makes an angle of 0 with a unit vector b. Then the unit vector ( a b) is [MP PET 99]. The perimeter of the triangle whose vertices have the position vectors
More informationClass : 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 informationBasic Quadrilateral Proofs
Basic Quadrilateral Proofs For each of the following, draw a diagram with labels, create the givens and proof statement to go with your diagram, then write a two-column proof. Make sure your work is neat
More informationRD Sharma Solutions for Class 10 th
RD Sharma Solutions for Class 10 th Contents (Click on the Chapter Name to download the solutions for the desired Chapter) Chapter 1 : Real Numbers Chapter 2 : Polynomials Chapter 3 : Pair of Linear Equations
More information3. AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is:
Solved Paper 2 Class 9 th, Mathematics, SA 2 Time: 3hours Max. Marks 90 General Instructions 1. All questions are compulsory. 2. Draw neat labeled diagram wherever necessary to explain your answer. 3.
More information8-6. a: 110 b: 70 c: 48 d: a: no b: yes c: no d: yes e: no f: yes g: yes h: no
Lesson 8.1.1 8-6. a: 110 b: 70 c: 48 d: 108 8-7. a: no b: yes c: no d: yes e: no f: yes g: yes h: no 8-8. b: The measure of an exterior angle of a triangle equals the sum of the measures of its remote
More informationGeometry CP Semester 1 Review Packet. answers_december_2012.pdf
Geometry CP Semester 1 Review Packet Name: *If you lose this packet, you may print off your teacher s webpage. If you can t find it on their webpage, you can find one here: http://www.hfhighschool.org/assets/1/7/sem_1_review_packet
More informationGeometry 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 informationChapter 3 Cumulative Review Answers
Chapter 3 Cumulative Review Answers 1a. The triangle inequality is violated. 1b. The sum of the angles is not 180º. 1c. Two angles are equal, but the sides opposite those angles are not equal. 1d. The
More informationA. 180 B. 108 C. 360 D. 540
Part I - Multiple Choice - Circle your answer: 1. Find the area of the shaded sector. Q O 8 P A. 2 π B. 4 π C. 8 π D. 16 π 2. An octagon has sides. A. five B. six C. eight D. ten 3. The sum of the interior
More information0110ge. Geometry Regents Exam Which expression best describes the transformation shown in the diagram below?
0110ge 1 In the diagram below of trapezoid RSUT, RS TU, X is the midpoint of RT, and V is the midpoint of SU. 3 Which expression best describes the transformation shown in the diagram below? If RS = 30
More information9. AD = 7; By the Parallelogram Opposite Sides Theorem (Thm. 7.3), AD = BC. 10. AE = 7; By the Parallelogram Diagonals Theorem (Thm. 7.6), AE = EC.
3. Sample answer: Solve 5x = 3x + 1; opposite sides of a parallelogram are congruent; es; You could start b setting the two parts of either diagonal equal to each other b the Parallelogram Diagonals Theorem
More informationSSC CGL Tier 1 and Tier 2 Program
Gurudwara Road Model Town, Hisar 9729327755 www.ssccglpinnacle.com SSC CGL Tier 1 and Tier 2 Program -------------------------------------------------------------------------------------------------------------------
More informationMATHEMATICS. (Two hours and a half) Answers to this Paper must be written on the paper provided separately.
CLASS IX MATHEMATICS (Two hours and a half) Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent
More informationKENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION
KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 02 F SESSING ENDING EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS IX Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA
More informationMOCKTIME.COM ONLINE TEST SERIES CORRESPONDENCE COURSE
GEOMETRY TRIANGLES AND THEIR PROPERTIES A triangle is a figure enclosed by three sides. In the figure given below, ABC is a triangle with sides AB, BC, and CA measuring c, a, and b units, respectively.
More informationHonors Geometry Mid-Term Exam Review
Class: Date: Honors Geometry Mid-Term Exam Review Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. 1. Classify the triangle by its sides. The
More informationSUMMATIVE ASSESSMENT II SAMPLE PAPER I MATHEMATICS
SUMMATIVE ASSESSMENT II SAMPLE PAPER I MATHEMATICS Class: IX Time: 3-3 ½ hours M.Marks:80 General Instructions: 1. All questions are compulsory 2. The question paper consists of 34 questions divided into
More informationright angle an angle whose measure is exactly 90ᴼ
right angle an angle whose measure is exactly 90ᴼ m B = 90ᴼ B two angles that share a common ray A D C B Vertical Angles A D C B E two angles that are opposite of each other and share a common vertex two
More informationTopic 2 [312 marks] The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths
Topic 2 [312 marks] 1 The rectangle ABCD is inscribed in a circle Sides [AD] and [AB] have lengths [12 marks] 3 cm and (\9\) cm respectively E is a point on side [AB] such that AE is 3 cm Side [DE] is
More information2. In ABC, the measure of angle B is twice the measure of angle A. Angle C measures three times the measure of angle A. If AC = 26, find AB.
2009 FGCU Mathematics Competition. Geometry Individual Test 1. You want to prove that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex. Which postulate/theorem
More informationBRAIN INTERNATIONAL SCHOOL TERM -II CLASS- IX SUB :- MATHS REVISION SHEET
BRAIN INTERNATIONAL SCHOOL TERM -II CLASS- IX 2017-18 SUB :- MATHS REVISION SHEET NUMBER SYSTEMS 1. Find three rational numbers between 2/7 and 3/7 2. Find two irrational numbers whose: (i)product is an
More informationClass 6 Geometry. Answer the questions. For more such worksheets visit (1) If AB and DE are parallel, find the value of ACB.
ID : in-6-geometry [1] Class 6 Geometry For more such worksheets visit www.edugain.com 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,
More informationSUMMATIVE 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 informationName: Class: Date: 5. If the diagonals of a rhombus have lengths 6 and 8, then the perimeter of the rhombus is 28. a. True b.
Indicate whether the statement is true or false. 1. If the diagonals of a quadrilateral are perpendicular, the quadrilateral must be a square. 2. If M and N are midpoints of sides and of, then. 3. The
More information