Year 9 Term 3 Homework

Similar documents
Chapter 3 Cumulative Review Answers

TRIANGLES CHAPTER 7. (A) Main Concepts and Results. (B) Multiple Choice Questions

9. 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.

Visit: ImperialStudy.com For More Study Materials Class IX Chapter 12 Heron s Formula Maths

Geometry. Midterm Review

6 CHAPTER. Triangles. A plane figure bounded by three line segments is called a triangle.

Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Ismailia Road Branch

Class IX Chapter 8 Quadrilaterals Maths

Class IX Chapter 8 Quadrilaterals Maths

Year 11 Math Homework

GM1.1 Answers. Reasons given for answers are examples only. In most cases there are valid alternatives. 1 a x = 45 ; alternate angles are equal.

Geometry Final Review. Chapter 1. Name: Per: Vocab. Example Problems

1. If two angles of a triangle measure 40 and 80, what is the measure of the other angle of the triangle?

CONGRUENCE OF TRIANGLES

Chapter (Circle) * Circle - circle is locus of such points which are at equidistant from a fixed point in

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

Honors Geometry Mid-Term Exam Review

QUESTION BANK ON STRAIGHT LINE AND CIRCLE

0114ge. Geometry Regents Exam 0114

GEO REVIEW TEST #1. 1. In which quadrilateral are the diagonals always congruent?

Geometry Honors Review for Midterm Exam

0113ge. Geometry Regents Exam In the diagram below, under which transformation is A B C the image of ABC?

(b) the equation of the perpendicular bisector of AB. [3]

Downloaded from

2. 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.

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

Triangles. 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. 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.

0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.

0811ge. Geometry Regents Exam

Chapter 8 Similar Triangles

0110ge. Geometry Regents Exam Which expression best describes the transformation shown in the diagram below?

0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below.

0609ge. Geometry Regents Exam AB DE, A D, and B E.

Geometry Honors: Midterm Exam Review January 2018

8-6. a: 110 b: 70 c: 48 d: a: no b: yes c: no d: yes e: no f: yes g: yes h: no

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:

1. How many planes can be drawn through any three noncollinear points? a. 0 b. 1 c. 2 d. 3. a cm b cm c cm d. 21.

Similarity of Triangle

9 th CBSE Mega Test - II

8-6. a: 110 b: 70 c: 48 d: a: no b: yes c: no d: yes e: no f: yes g: yes h: no

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

UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).

Use this space for computations. 1 In trapezoid RSTV below with bases RS and VT, diagonals RT and SV intersect at Q.

Geometry Midterm Exam Review 3. Square BERT is transformed to create the image B E R T, as shown.

0610ge. Geometry Regents Exam The diagram below shows a right pentagonal prism.

Name: 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.

0612ge. Geometry Regents Exam

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.

Properties of the Circle

Nozha Directorate of Education Form : 2 nd Prep

UNIT 1: SIMILARITY, CONGRUENCE, AND PROOFS. 1) Figure A'B'C'D'F' is a dilation of figure ABCDF by a scale factor of 1. 2 centered at ( 4, 1).

1 What is the solution of the system of equations graphed below? y = 2x + 1

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:


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

2012 GCSE Maths Tutor All Rights Reserved

Indicate whether the statement is true or false.

Practice Test Student Answer Document

JEFFERSON MATH PROJECT REGENTS AT RANDOM

The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION COURSE II. Wednesday, August 16, :30 to 11:30 a.m.

VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER)

Exercise. and 13x. We know that, sum of angles of a quadrilateral = x = 360 x = (Common in both triangles) and AC = BD

Part (1) Second : Trigonometry. Tan

Honors Geometry Midterm Questions

OBJECTIVE TEST. Answer all questions C. N3, D. N3, Simplify Express the square root of in 4

Geometry Honors Final Exam Review June 2018

Alg. (( Sheet 1 )) [1] Complete : 1) =.. 3) =. 4) 3 a 3 =.. 5) X 3 = 64 then X =. 6) 3 X 6 =... 7) 3

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

Triangles. Chapter Flowchart. The Chapter Flowcharts give you the gist of the chapter flow in a single glance.

AREAS OF PARALLELOGRAMS AND TRIANGLES

Chapter - 7. (Triangles) Triangle - A closed figure formed by three intersecting lines is called a triangle. A

Geometry - Semester 1 Final Review Quadrilaterals

iii (a, c), (a, e), (c, e), (b, d), (b, f), (d, f), (l, h), (l, j), (h, j), (g, i), (g, k), (i, k)

Class IX - NCERT Maths Exercise (10.1)

CBSE Class IX Syllabus. Mathematics Class 9 Syllabus

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?

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

Class IX Chapter 7 Triangles Maths

Pre RMO Exam Paper Solution:

End of Course Review

EXERCISE 10.1 EXERCISE 10.2

Unit 4-Review. Part 1- Triangle Theorems and Rules

Geometry Cumulative Review

JEFFERSON MATH PROJECT REGENTS AT RANDOM

1 st Preparatory. Part (1)

9. Areas of Parallelograms and Triangles

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

Rhombi, Rectangles and Squares

Class IX Chapter 7 Triangles Maths. Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure).

Pythagorean Theorem a= 6.4, b = 12, c = a = 2.1, b = 7.2, c = 7.5

SOLUTIONS SECTION A SECTION B

HIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 2/3 UNIT (COMMON) Time allowed Three hours (Plus 5 minutes reading time)

5. Using a compass and straightedge, construct a bisector of the angle shown below. [Leave all construction marks.]

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

0116ge. Geometry Regents Exam RT and SU intersect at O.

CAREER POINT PRE FOUNDATION DIVISON CLASS-9. IMO Stage-II Exam MATHEMATICS Date :

Honors Geometry Review Exercises for the May Exam

TERMWISE SYLLABUS SESSION CLASS-IX SUBJECT : MATHEMATICS. Course Structure. Schedule for Periodic Assessments and CASExam. of Session

CHAPTER 7 TRIANGLES. 7.1 Introduction. 7.2 Congruence of Triangles

Transcription:

Yimin Math Centre Year 9 Term 3 Homework Student Name: Grade: Date: Score: Table of contents 5 Year 9 Term 3 Week 5 Homework 1 5.1 Geometry (Review)................................... 1 5.1.1 Angle sum of a triangle............................. 1 5.1.2 Angle sum of a quadrilateral.......................... 2 5.1.3 Tests for congruent triangles.......................... 3 5.1.4 Congruence proofs............................... 4 5.1.5 Deductive reasoning and congruent triangles................. 6 5.1.6 Problem solving................................ 8 5.2 Math challenge..................................... 9 5.3 Miscellaneous exercise................................. 10 This edition was printed on October 6, 2010. Camera ready copy was prepared with the L A TEX2e typesetting system. Year 9 Term 3 Homework

Year 9 Term 3 Week 5 Homework Page 1 of 13 5 Year 9 Term 3 Week 5 Homework 5.1 Geometry (Review) 5.1.1 Angle sum of a triangle The angle sum of a triangle is 180. The exterior angle of a triangle is equal to the sum of two interior opposite angles. In an equilateral triangle all angles are 60. In an isosceles triangle, the equal angles are opposite the equal sides. In any triangle, the longest side is opposite the largest angle, while the shortest side is opposite the smallest angle. Exercise 5.1.1 Find the value of the pronumeral in each of the following figures: 1. Find the value of k. 2. If the EF G is a isosceles triangle, find the value of w. 3. Find the value of n.

Year 9 Term 3 Week 5 Homework Page 2 of 13 5.1.2 Angle sum of a quadrilateral Exercise 5.1.2 Find the value of the pronumeral in each of the following figures, giving reasons. 1. x =, v =,w = 2. y =, z = 3. u =, v = 4. x =

Year 9 Term 3 Week 5 Homework Page 3 of 13 5.1.3 Tests for congruent triangles Two triangles are said to be congruent if they have exactly the same size and shape. If two triangle are congruent, then: 1. the matching sides are equal in length 2. the matching angles are equal in size 3. the figures are equal in area. Tests: If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent (SSS). If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent (SAS). If two angles and one side of triangle are equal to two angles and the matching side of another triangle, then the two triangles are congruent (ASA or AAS). If the hypotenuse and a second side of one right-angled triangle are equal to the hypotenuse and a second side of another right-angled triangle, then the two triangles are congruent (RHS).

Year 9 Term 3 Week 5 Homework Page 4 of 13 5.1.4 Congruence proofs To prove that two triangles are congruent: identify the triangles that are being used in the proof name the three pairs of equal sides or angles name the congruent triangle given the vertices of the triangles in matching order and state the congruence test used. Example 5.1.1 PQRS is a rectangle and TS = TR, Prove that T P S T QR. Solution: in T P S and T QR. Solution: TS = TR (given) T P S = T QR = 90 (All angles are right angles in a rectangle) PS = QR (opposite sides of a rectangle are equal) T P S T QR (RHS) Exercise 5.1.3 Prove that P QR T SR.

Year 9 Term 3 Week 5 Homework Page 5 of 13 Exercise 5.1.4 1. In the XY W, XW = XY and XZ W Y. Prove that XW Z XY Z. 2. KLMN is a parallelogram. Prove that KLN M N L. 3. STUV is a parallelogram. SW = XU and VW = XT. Prove that SV W UT X

Year 9 Term 3 Week 5 Homework Page 6 of 13 5.1.5 Deductive reasoning and congruent triangles If one triangle is congruent to another, then the matching sides and angles in those triangle must be equal. The equivalence of these matching sides and angles can be used to prove that: two lines are parallel two lines are perpendicular a line bisects an interval a line bisects an angle a given triangle is isosceles a given quadrilateral is a parallelogram, a rectangle, a rhombus or a square. Example 5.1.2 If T US is an isosceles triangle, UP ST and SQ T U, prove that the P RS QRU and hence prove that SRU is isosceles. Solution: In P RS and QRU PS = QU (given) RP S = RQU = 90 (UP ST and SQ T U) P RS = QRU (vertical opposite angles are equal) P RS QRU (AAS) RS = RU (matching side of congruent s) SRU is isosceles.

Year 9 Term 3 Week 5 Homework Page 7 of 13 Exercise 5.1.5 For each of the following prove that the two triangles are congruent, hence find the value of the pronumeral. 1. T U W X and T U = W X. Prove T UV V W X 2. CF DE and CF = DE. Prove that CEF CDE 3. EF F H, GH F H and EF = GH. Prove that GF H EF H

Year 9 Term 3 Week 5 Homework Page 8 of 13 5.1.6 Problem solving Exercise 5.1.6 1. Is a rhombus a regular polygon? Why or why not? 2. Calculate the interior angle sum of each of these regular polygons, then find the size of their interior angles: (a) decagon (b) dodecagon 3. Find the size of the exterior angles in a regular: (a) pentagon (b) nonagon 4. How many sides has a regular polygon with: (a) exterior angles measuring 15 (b) interior angles measuring 175

Year 9 Term 3 Week 5 Homework Page 9 of 13 5.2 Math challenge Exercise 5.2.1 1. The area of ABC is 50 cm 2. Point D lies on side BA, DA = 6 cm and BA = 25cm. Find the area of CBD. 2. In the following trapezium, DC//AB, AC CB, AC = CB and BA = BD. Find the ABD. 3. In a magic square the rows, columns and diagonals each add up to the same number. In this magic square the numbers 39, 47, 55, 63 67 and 71 are missing. What number does? stand for?

Year 9 Term 3 Week 5 Homework Page 10 of 13 5.3 Miscellaneous exercise Exercise 5.3.1 1. The exterior angles of a pentagon are 2x, (2x + 3), (3x + 12), (3x 20) and (x + 35). Calculate the following: (a) the value of x, (b) the smallest interior angle, (c) the smallest exterior angle. 2. Evaluate the following: (a) 6 [108 ( 17 + 8)] 36 + 12 (b) (2 1 3 + 1 2 9 ) 2 2 5 (c) 12 2 2 4 + 7 2 3. A clock gains 12 minutes 15 seconds in one week. How many days will it take to gain 1 hour and 45 minutes?

Year 9 Term 3 Week 5 Homework Page 11 of 13 Exercise 5.3.2 1. Given that the two triangles are similar, form an equation in terms of x and solve it. 2. In the diagram shown below, BC is parallel to ED. AB = 6 cm, BD = 2 cm, AC = (x + 5) cm and CE = x cm. Find the value of x. 3. Given that 3 x 4 and 2 y 6, find the following: (a) the least possible value of x y. (b) the least possible value of xy.

Year 9 Term 3 Week 5 Homework Page 12 of 13 Exercise 5.3.3 1. If the solution of x 2 + bx + 36 = 0 are integers, find the number of integer values b can have. 2. There are exactly 3 integers x satisfying the inequality x 2 + bx + 2 0. How may integer value of b are possible? 3. If 2 = 1 + 1, find the value of x. 2+ 1 2+x 4. How many real solution of the equation x 2 + x 3 + 1 + x = 1 can have? 5. A number is added to one third of itself. The result is 108. What is the number?

Year 9 Term 3 Week 5 Homework Page 13 of 13 Exercise 5.3.4 The rhombus ABCD has a perimeter of 68 cm. The diagonals AC and BD intersect at P and ABC = 68. 1. Find the size of ABP. 2. Find the length of the diagonal AC, correct to one decimal place. Exercise 5.3.5 1. A chord AB of length 16 cm is drawn in a circle with centre O and area 100π cm 2. Find the size of the angle that the chord AB subtends at the centre of the circle (correct to nearest minutes). 2. ABC is an equilateral triangle with sides 12 cm long. D is a point on BC, 4 cm from B. Find the size of ADC (correct to nearest minutes). 3. Find the value of x correct to one decimal place.

2024 © sciencedocbox.com Privacy Policy | Terms of Service | Feedback