Revision Congruency & Similarity Area & Volume of Similar Figures Scales & Maps
|
|
- Eleanor Simmons
- 5 years ago
- Views:
Transcription
1 Question 1: In the quadrilateral ABCD, the diagonals AC and BD intersect at X. AX = BX and DX = CX. AB is parallel to DC. a) Name a pair of congruent triangles. b) Name a pair of similar triangles. a) AXD & BXC (SAS) b) A X B & C X D
2 Question 2: In the diagram, CEFG is a rectangle and ABCD is a square. ABG is a straight line. a) Show that DCE BCG. b) Prove that triangle DCE is congruent to triangle BCG. c) Hence show that CEFG is a square. a) DCB 90 DCE 90 ECB BCG 90 ECG DCE BCG b) DC BC EDC GBC DCE BCG By ASA, DCE is congruent to BCG c) Since DCE is congruent to BCG, EC = GC = FG = EF CEFG is a square
3 Question 3: In the diagram, AFB, AEC and FED are straight lines. DE = 7 cm, FED//BC, AFB//DC and AE = EC. a) Name a triangle that is congruent to AEF. State the reasons for its congruency. b) Name a triangle that is similar to AEF. State the reasons for its similarity. c) Find the length of BC. a) b) CED (ASA) ACB (AAA) c) AE AC FE BC 1 2 FE BC BC BC 14cm
4 Question 4: In the diagram, ADC is a straight line and ABD BCD. a) Prove that triangle ABD is similar to triangle ACB. State your reasons. b) AD = 4 cm, BD = 6 cm and BC = 9 cm. i. Prove that triangle ABD is an isosceles triangle. ii. Find BAD. a) ABD = ACB (given) BAD = CAB (common) BDA CBA AAA, both are similar b) i. AD AB BD CB AB 6 9 AB 6 AB = BD = 6 ABD is an isosceles ii. Using cosine rule, (6)(4)cos cosâ 1 3  70.5 (1dp)
5 Question 5: In the figure below, rectangle ABCD is reduced to rectangle EFGH. From the information above, find the value of p. 4 p p p p 18 p 4.5cm
6 Question 6: Given that RP = 9 cm and PQ = 3 cm, a) show that TPQ is similar to SPR. b) calculate area of TPQ area of SPR as a fraction. c) QPT is mapped onto SPR by enlargement. State the scale factor of enlargement. a) TPQ SPR (vertically opposite ) QTP RSP (same segment) TPQ is similar to SPR (By AAA) b) ( 3 9 )2 1 9 c) 3
7 Question 7: In the diagram below, AB = 8 cm, BC = 5 cm, AE = 10 cm and BE // CD. a) Show that triangle ABE is similar to triangle ACD. b) Find the value of i. BE. CD ii. ED. iii. area of ΔABE. area of ΔACD iv. v. area of ΔABE. area of trapezium BCDE area of ΔBCD. area of ΔABD a) ABE = ACD AED = ADC By AAA, ABE is similar to ACD b) iv. BE CD AB AC 8 13 i. ( 8 13 ) v. AE AD = AB AC AD AE = AC AB AD cm ED = 6.25cm ii iii. BE:CD 8:13 21 parts parts
8 Question 8: In the diagram below, D and E are two points on ABC in which DE // BC. Given that CD and BE intersect at F. AE = 4 cm and EC = 12 cm. a) Show that triangles ABC and ADE are similar. b) Find the length of DE if BC = 18 cm. c) Find the value of area of ADE. area of quadrilate ral DBCE a) ADE = ABE AED = ACB DAE = BAC By AAA, ABC is similar to ADE b) DE BC = AE AC DE DE = 4.5 c) ADE ABC ( 1 4 ) ADE DBCE 1 15
9 Question 9: The two containers shown in the diagram are geometrically similar. Their height are 24 cm and 80 cm respectively. a) The diameter of the base of the smaller container is 15 cm. Calculate the diameter of the base of the larger container. b) Find the ratio of the volume of the smaller container to the larger container. Give your answer as a fraction in its lowest term. c) The containers are completely filled with rice. The larger container can hold 250 kg of rice. Calculate the mass of rice that the smaller container can hold. a) Large Large 50cm b) ( 3 10 ) c) 27 : kg:250kg
10 Question 10: The two containers shown in the diagram are geometrically similar. Their heights are 20 cm and 50 cm. a) The diameter of the base of the larger container is 14 cm. Calculate the diameter of the base of the smaller container. b) The containers are completely filled with sand. Given that the smaller container holds 2.8 kg of sand, estimate the mass of sand the larger container holds. a) smaller smaller b) ( 2 5 ) : :43.75kg
11 Question 11: Two cups are geometrically similar in shape. The total surface area of the smaller cup is 8 cm 2 and the total surface area of the larger cup is 18 cm 2. a) Find the ratio between the heights of the two cups. b) The smaller cup fruit juice is sold at $0.80 per cup. Adam wishes to buy the larger cup fruit juice. How much will it cost him? a) 8 :18 4 : 9 ht 2 :3 b) V1 V2 ( 2 3 ) :27 $0.80 : $2.70
12 Question 12: The base areas of two geometrically similar vases are in the ratio of 16 : 25. a) The curved surface area of the larger vase is 625 cm 2. Find the curved surface area of the smaller vase. b) If the mass of the smaller vase is 4.8 kg, find the mass of the larger vase. a) 16 : :625 b) ht 1 ht V1 V2 4.8kg x ( 4 5 )3 4.8 x x 9.375kg
13 Question 13: The diagram below shows a cup in the form of an inverted cone of height 15 cm. Water is poured into the cup until the height of the water is 3 cm. If the volume of the water is 12 cm 3, find the volume of the unfilled space of the cup. ( 3 15 )3 ( 1 5 ) :125 12:?? 1500 Empty space = 1488cm 3
14 Question 14: The following two thermo flasks are geometrically similar and have capacities of 432 ml and 2 l. a) Find, in its simplest integer form, the ratio of the height of the smaller thermo flask to the height of the larger thermo flask. b) The base area of the smaller thermo flask is 45 cm 2. Find the base area of the larger thermo flask. c) Given the height of the larger thermo flask is 32 cm, find the height of the smaller thermo flask. a) 432: :125 ( ) 3 5 3:5 b) ( 3 5 ) :25 45 :125 c) 3: :32
15 Question 15: A map is drawn to a scale of 1 : a) An expressway leading to East Coast Park is represented by a line of length 5.6 cm on the map. Calculate the actual length of the expressway, giving your answer in kilometres. b) If the actual area of the East Coast Park is 5 km 2, find the area of East Coast Park on the map in cm 2. a) 1 : : 500m 1: 0.5km 5.6 : 2.8km b) 1 : 0.5 km 1 2 : 0.25km 2 20cm 2 : 5km 2
16 Question 16: A map is drawn to a scale of 1 cm : 8 km. a) Write down the scale in the form 1 : n. b) On the map, two towns are 3.2 cm apart. What is the actual distance between the two towns, in kilometres? c) A plot of land has an area of 96 km 2. Find the area on the map in square centimetres that represents this actual area. a) 1cm :8000m 1cm :800000cm b) 1cm :8km 3.2cm :25.6km c) 1cm km 2 1cm 2 :64km 2 1.5cm 2 :96km 2
17 Question 17: An actual ground distance of 5 km is represented by a distance of 2 cm on a city map. a) Express the scale of the map in the form 1 : n. b) If the distance between two buildings on the map is 15 cm find their actual distance on the ground in km. c) If the area of a stadium is 0.3 cm 2 on the map, find its actual area in km 2. a) 2cm :5km 2cm :5000m 2cm :500000cm 1cm : cm b) 2cm :5km 15cm :37.5km c) 2 2 cm 2 :5 2 km 2 4cm 2 :25km 2 0.3cm 2 :1.875km 2
18 Question 18: An actual area of a pond of 125 m 2 is represented by 5 cm 2 on a map. Calculate the a) scale of the map in the form 1 : n. b) length of a line on the map, which represents a path 13 m long. a) 5cm 2 :125m 2 1cm 2 :25m 2 1cm:5m 1cm:500cm b) 1cm :5m 2.6cm:13m
19 Question 19: An actual region of a plot of land 36 km 2 is represented by an area of 4 cm 2 on the map. a) If the area of a town on the map is 0.3 cm 2, find its actual area in km 2. b) Find the scale of the map in the form 1 : n. c) Find the length on the map which represents an actual length of 4.5 km. a) 4cm 2 :36km 2 1cm 2 :9km 2 0.3cm 2 :2.7km 2 b) 1cm :3km 1cm : 3000m 1cm : cm c) 1cm :3km 1.5cm : 4.5km
20 Question 20: The actual area of a pond which is16 km 2 is represented on map A by an area of 400 cm 2. a) If map A is drawn to a scale of 1 : k, find the value of k. b) The distance of two locations on map A is 8.6 cm. Find the distance of the same two locations on map B which has a scale of 1 cm : 0.4 km. c) State which map has a longer map distance of the two locations. a) 400cm 2 :16km 2 25cm 2 :1km 2 5cm:1km 5cm:1000m 5cm:100000cm 1cm:20000cm b) 1cm :20000cm 8.6cm:172000cm 1cm:0.4km 1cm:400m 1cm:40000cm 4.3cm:172000cm c) 8.6cm, Map A
21 Revision Accomplished!
Geometry Problem Solving Drill 08: Congruent Triangles
Geometry Problem Solving Drill 08: Congruent Triangles Question No. 1 of 10 Question 1. The following triangles are congruent. What is the value of x? Question #01 (A) 13.33 (B) 10 (C) 31 (D) 18 You set
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 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 informationSimilarity of Triangle
Similarity of Triangle 95 17 Similarity of Triangle 17.1 INTRODUCTION Looking around you will see many objects which are of the same shape but of same or different sizes. For examples, leaves of a tree
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 informationA plane can be names using a capital cursive letter OR using three points, which are not collinear (not on a straight line)
Geometry - Semester 1 Final Review Quadrilaterals (Including some corrections of typos in the original packet) 1. Consider the plane in the diagram. Which are proper names for the plane? Mark all that
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 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 information0615geo. Geometry CCSS Regents Exam In the diagram below, congruent figures 1, 2, and 3 are drawn.
0615geo 1 Which object is formed when right triangle RST shown below is rotated around leg RS? 4 In the diagram below, congruent figures 1, 2, and 3 are drawn. 1) a pyramid with a square base 2) an isosceles
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 informationSMT 2018 Geometry Test Solutions February 17, 2018
SMT 018 Geometry Test Solutions February 17, 018 1. Consider a semi-circle with diameter AB. Let points C and D be on diameter AB such that CD forms the base of a square inscribed in the semicircle. Given
More informationGeometry - Semester 1 Final Review Quadrilaterals
Geometry - Semester 1 Final Review Quadrilaterals 1. Consider the plane in the diagram. Which are proper names for the plane? Mark all that apply. a. Plane L b. Plane ABC c. Plane DBC d. Plane E e. Plane
More informationCONGRUENCE OF TRIANGLES
Congruence of Triangles 11 CONGRUENCE OF TRIANGLES You might have observed that leaves of different trees have different shapes, but leaves of the same tree have almost the same shape. Although they may
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 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 informationPostulates and Theorems in Proofs
Postulates and Theorems in Proofs A Postulate is a statement whose truth is accepted without proof A Theorem is a statement that is proved by deductive reasoning. The Reflexive Property of Equality: a
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 information0609ge. Geometry Regents Exam AB DE, A D, and B E.
0609ge 1 Juliann plans on drawing ABC, where the measure of A can range from 50 to 60 and the measure of B can range from 90 to 100. Given these conditions, what is the correct range of measures possible
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 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 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 informationGEO REVIEW TEST #1. 1. In which quadrilateral are the diagonals always congruent?
GEO REVIEW TEST #1 Name: Date: 1. In which quadrilateral are the diagonals always congruent? (1) rectangle (3) rhombus 4. In the accompanying diagram, lines AB and CD intersect at point E. If m AED = (x+10)
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 informationEOC Review MC Questions
Geometry EOC Review MC Questions Name Date Block You must show all work to receive full credit. - For every 5 answers that are correct, you may receive 5 extra points in the quiz category for a total of
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 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 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 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 informationINSTRUCTIONS. F.3 2 nd Maths Examination (1011) P1/14
INSTRUCTIONS 1. The total mark of this paper is 100. 2. This paper consists of THREE sections, A, B and C. 3. Attempt ALL questions in this paper. Write your answers in the spaces provided in this Question-Answer
More information1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT.
1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would prove l m? 1) 2.5 2) 4.5 3)
More informationHigher. Ch 19 Pythagoras, Trigonometry and Vectors. Bilton
Higher Ch 19 Pythagoras, Trigonometry and Vectors Bilton Questions Q1. Triangle ABC has perimeter 20 cm. AB = 7 cm. BC = 4 cm. By calculation, deduce whether triangle ABC is a right angled triangle. (Total
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 informationTriangles. Example: In the given figure, S and T are points on PQ and PR respectively of PQR such that ST QR. Determine the length of PR.
Triangles Two geometric figures having the same shape and size are said to be congruent figures. Two geometric figures having the same shape, but not necessarily the same size, are called similar figures.
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 informationPage 1 of 11 Name: 1) Which figure always has exactly four lines of reflection that map the figure onto itself? A) rectangle B) square C) regular octagon D) equilateral triangle ee4caab3 - Page 1 2) In
More informationIB MYP Unit 6 Review
Name: Date: 1. Two triangles are congruent if 1. A. corresponding angles are congruent B. corresponding sides and corresponding angles are congruent C. the angles in each triangle have a sum of 180 D.
More informationGeometry Midterm Exam Review 3. Square BERT is transformed to create the image B E R T, as shown.
1. Reflect FOXY across line y = x. 3. Square BERT is transformed to create the image B E R T, as shown. 2. Parallelogram SHAQ is shown. Point E is the midpoint of segment SH. Point F is the midpoint of
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 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 informationDay 6: Triangle Congruence, Correspondence and Styles of Proof
Name: Day 6: Triangle Congruence, Correspondence and Styles of Proof Date: Geometry CC (M1D) Opening Exercise Given: CE bisects BD Statements 1. bisects 1.Given CE BD Reasons 2. 2. Define congruence in
More informationMaharashtra State Board Class X Mathematics Geometry Board Paper 2015 Solution. Time: 2 hours Total Marks: 40
Maharashtra State Board Class X Mathematics Geometry Board Paper 05 Solution Time: hours Total Marks: 40 Note:- () Solve all questions. Draw diagrams wherever necessary. ()Use of calculator is not allowed.
More informationClass IX Chapter 7 Triangles Maths. Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure).
Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? In ABC and ABD, AC = AD (Given) CAB = DAB (AB bisects
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 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 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 information0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below.
Geometry Regents Exam 011 011ge 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would
More informationChapter 7. Geometric Inequalities
4. Let m S, then 3 2 m R. Since the angles are supplementary: 3 2580 4568 542 Therefore, m S 42 and m R 38. Part IV 5. Statements Reasons. ABC is not scalene.. Assumption. 2. ABC has at least 2. Definition
More informationAnswer Key. 9.1 Parts of Circles. Chapter 9 Circles. CK-12 Geometry Concepts 1. Answers. 1. diameter. 2. secant. 3. chord. 4.
9.1 Parts of Circles 1. diameter 2. secant 3. chord 4. point of tangency 5. common external tangent 6. common internal tangent 7. the center 8. radius 9. chord 10. The diameter is the longest chord in
More informationQuestion 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD?
Class IX - NCERT Maths Exercise (7.1) Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? Solution 1: In ABC and ABD,
More informationClass IX Chapter 7 Triangles Maths
Class IX Chapter 7 Triangles Maths 1: Exercise 7.1 Question In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? In ABC and ABD,
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 informationJEFFERSON MATH PROJECT REGENTS AT RANDOM
JEFFERSON MATH PROJECT REGENTS AT RANDOM The NY Geometry Regents Exams Fall 2008-August 2009 Dear Sir I have to acknolege the reciept of your favor of May 14. in which you mention that you have finished
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 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 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 informationSOLUTIONS TO EXERCISES FOR. MATHEMATICS 133 Part 4. Basic Euclidean concepts and theorems
SOLUTIONS TO EXERCISES FOR MATHEMATICS 133 Part 4 Winter 2009 NOTE ON ILLUSTRATIONS. Drawings for several of the solutions in this file are available in the following file: http://math.ucr.edu/ res/math133/math133solutions04.figures.f13.pdf
More informationGEOMETRY (Common Core)
GEOMETRY (COMMON CORE) The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY (Common Core) Tuesday, June 2, 2015 1:15 to 4:15 p.m., only Student Name: School Name: The possession
More information*1 (a), leaving the answer in recurring decimal.
*1 (a) Calculate 3 2 72, leaving the answer in recurring decimal. (7 3)3.3 Answer (a) [1] (b) Write your answer to part (a) correct to 2 significant figures. Answer (b) [1] *2 If find the value of Answer
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 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 informationGiven. Segment Addition. Substitution Property of Equality. Division. Subtraction Property of Equality
Mastery Test Questions (10) 1. Question: What is the missing step in the following proof? Given: ABC with DE AC. Prove: Proof: Statement Reason
More informationCreated by T. Madas. Candidates may use any calculator allowed by the regulations of this examination.
IYGB GCE Mathematics MP1 Advanced Level Practice Paper P Difficulty Rating: 3.9900/1.3930 Time: 2 hours Candidates may use any calculator allowed by the regulations of this eamination. Information for
More informationPractice Test Student Answer Document
Practice Test Student Answer Document Record your answers by coloring in the appropriate bubble for the best answer to each question. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
More information2012 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 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 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 informationExercises for Unit I I I (Basic Euclidean concepts and theorems)
Exercises for Unit I I I (Basic Euclidean concepts and theorems) Default assumption: All points, etc. are assumed to lie in R 2 or R 3. I I I. : Perpendicular lines and planes Supplementary background
More informationMathematical Formulae. r 100. Total amount = Curved surface area of a cone = rl. Surface area of a sphere = Volume of a cone = Volume of a sphere =
1 Mathematical Formulae Compound Interest Total amount = r P ( 1 ) 100 n Mensuration Curved surface area of a cone = rl Surface area of a sphere = 2 4 r Volume of a cone = 1 3 r 2 h Volume of a sphere
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level *5539296252* MATHEMATICS (SYLLABUS D) 4024/11 Paper 1 October/November 2011 2 hours Candidates answer
More informationProperties 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 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 informationCAREER POINT. PRMO EXAM-2017 (Paper & Solution) Sum of number should be 21
PRMO EXAM-07 (Paper & Solution) Q. 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? Sum
More informationClass 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 informationSUMMATIVE 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 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 informationAREAS OF PARALLELOGRAMS AND TRIANGLES
15 MATHEMATICS AREAS OF PARALLELOGRAMS AND TRIANGLES CHAPTER 9 9.1 Introduction In Chapter 5, you have seen that the study of Geometry, originated with the measurement of earth (lands) in the process of
More informationCircle and Cyclic Quadrilaterals. MARIUS GHERGU School of Mathematics and Statistics University College Dublin
Circle and Cyclic Quadrilaterals MARIUS GHERGU School of Mathematics and Statistics University College Dublin 3 Basic Facts About Circles A central angle is an angle whose vertex is at the center of the
More informationPre RMO Exam Paper Solution:
Paper Solution:. 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? Sum of Digits Drivable
More informationEnd of Course Review
End of Course Review Geometry AIR Test Mar 14 3:07 PM Test blueprint with important areas: Congruence and Proof 33 39% Transformations, triangles (including ASA, SAS, SSS and CPCTC), proofs, coordinate/algebraic
More informationCONGRUENCE AND SIMILARITY
CONGRUENCE ND SIMILRITY 1.1CONGRUENT FIGURES The figures that have the same size and the same shape, i.e. one shape fits exactly onto other is called Congruent figures. CONGRUENT TRINGLES: 1. Two triangles
More informationMathematics. 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 informationJEFFERSON MATH PROJECT REGENTS AT RANDOM
JEFFERSON MATH PROJECT REGENTS AT RANDOM The NY Geometry Regents Exams Fall 2008-January 2010 Dear Sir I have to acknolege the reciept of your favor of May 14. in which you mention that you have finished
More informationNAME: Mathematics 133, Fall 2013, Examination 3
NAME: Mathematics 133, Fall 2013, Examination 3 INSTRUCTIONS: Work all questions, and unless indicated otherwise give reasons for your answers. If the problem does not explicitly state that the underlying
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 informationRevision Question Bank
Revision Question Bank Triangles 1. In the given figure, find the values of x and y. Since, AB = AC C = B [angles opposite to the equal sides are equal] x = 50 Also, the sum of all angles of a triangle
More informationGeometry Facts Circles & Cyclic Quadrilaterals
Geometry Facts Circles & Cyclic Quadrilaterals Circles, chords, secants and tangents combine to give us many relationships that are useful in solving problems. Power of a Point Theorem: The simplest of
More informationExercises for Unit V (Introduction to non Euclidean geometry)
Exercises for Unit V (Introduction to non Euclidean geometry) V.1 : Facts from spherical geometry Ryan : pp. 84 123 [ Note : Hints for the first two exercises are given in math133f07update08.pdf. ] 1.
More informationPLC Papers. Created For:
PLC Papers Created For: Area of a Triangle 2 Grade 7 Objective: Know and apply the formula A = ½absinC to calculate the area, sides or angles of a triangle Question 1. AB = 8cm BC = 14cm Angle ABC = 106
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 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 informationGeometry Regents Practice Midterm
Class: Date: Geometry Regents Practice Midterm Multiple Choice Identify the choice that best completes the statement or answers the question. 1. ( points) What is the equation of a line that is parallel
More informationQ4. In ABC, AC = AB and B = 50. Find the value of C. SECTION B. Q5. Find two rational numbers between 1 2 and.
SUMMATIVE ASSESSMENT 1 (2013 2014) CLASS IX (SET I) SUBJECT : MATHEMATICS Time: 3 hours M.M. : 90 General Instructions : (i) All questions are compulsory. (ii) The question paper consists of 31 questions
More informationGeometry 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(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 informationTriangle 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 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 information(A) 2S + 3 (B) 3S + 2 (C) 3S + 6 (D) 2S + 6 (E) 2S + 12
1 The sum of two numbers is S Suppose 3 is added to each number and then each of the resulting numbers is doubled What is the sum of the final two numbers? (A) S + 3 (B) 3S + (C) 3S + 6 (D) S + 6 (E) S
More informationMATHEMATICS GRADE 12 SESSION 18 (LEARNER NOTES)
MATHEMATICS GRADE 1 SESSION 18 (LEARNER NOTES) TOPIC 1: TWO-DIMENSIONAL TRIGONOMETRY Learner Note: Before attempting to do any complex two or three dimensional problems involving trigonometry, it is essential
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 information