Geometry Test A PDF

# ESSENTIAL MATHEMATICS ## FOR THE AUSTRALIAN CURRICULUM SECOND EDITION ### Chapter 7: Geometry ### Test A (40 marks) **Name:**_____________________ **Part A - Multiple-choice (10 marks)** **1** Which of the following pairs of angles are complementary? A. 8°, 192° B. 16°, 84° C. 27°, 63° D. 35°...

# ESSENTIAL MATHEMATICS ## FOR THE AUSTRALIAN CURRICULUM SECOND EDITION ### Chapter 7: Geometry ### Test A (40 marks) **Name:**_____________________ **Part A - Multiple-choice (10 marks)** **1** Which of the following pairs of angles are complementary? A. 8°, 192° B. 16°, 84° C. 27°, 63° D. 35°, 45° E. 71°, 109° **2** The given triangle is: The image is of a triangle that has two sides marked with a line, meaning they both have an equal length. One of the angles is 40°. A. acute scalene B. acute isosceles C. right-angled isosceles D. obtuse scalene E. obtuse isosceles **3** The pair of lines in the following diagram are: The image is of two parallel lines cut by a transversal line. One of the angles between the transversal and a parallel line is 115°, while the other is 75°. A. parallel, since cointerior angles are supplementary B. parallel, since alternate angles are supplementary C. parallel, since corresponding angles are supplementary D. not parallel, since cointerior angles are not supplementary E. not parallel, since alternate angles are not supplementary **4** In this diagram, $\angle ABC$ is equal to: The image is of two skew lines cut by a transversal line. The angle between first skew line relative to the transversal is 35° and the angle between the second skew line relative to the transversal is 29°. A. 29° B. 35° C. 64° D. 84° E. 96° **5** A quadrilateral that has two pairs of parallel sides and whose sides are all of equal length is a: A. parallelogram B. rhombus C. trapezium D. rectangle E. kite **6** The value of x in the following diagram is: The figure in the image is of a hexagon with all sides of equal length. The angle x is an exterior angle to one of the vertices. A. 30° B. 36° C. 45° D. 60° E. 120° For questions 7 and 8, select which congruence test proves that the given pair of triangles is congruent. **7** The image shows two right triangles. A. SSS B. SAS C. AAS D. AAA E. RHS **8** The image is of two triangles that are the mirror opposite of each other. The side lengths are shown by tick marks which show the equality of lengths of corresponding sides. A. SSS B. SAS C. AAS D. AAA E. RHS **9** Which similarity test proves that the given pair of triangles is similar? The image shows two triangles with interior angles 45°, 70° and 65°, 70°. A. SSS B. SAS C. AAS D. AAA E. RHS **10** Gareth wishes to determine the width of the river shown in the diagram without crossing it. He places four markers as shown. The width of the river is: The image depicts a river with markers placed in the water and on the river bank. A. 24 m B. 28 m C. 30 m D. 32 m E. 36 m **Part B - Short-answer (23 marks)** **1** Find the value of each pronumeral. *a)* The image is of a right triangle. One of the angles is shown as 40°. Find a. *b)* The image is of a triangle where one of the angles is 120°. Find b. *c)* The image shows two lines intersecting each other. The angles relative to line 1 is 63° and 45° respectively. Find c. *d)* The image shows an equilateral triangle. Find d. (4 x 1 = 4 marks) **2** Find the value of each of the pronumerals. Give reasons for your answers. *a)* The image shows 2 parallel lines cut by a transversal. One of the angles between the first parallel line and the transversal is 80°. Find a. *b)* The image shows 2 parallel lines cut by a traversal. One of the angles between the first parallel line and the transversal is 116°. Find c and d. (2 + 2 = 4 marks) **3** Find the value of the pronumeral in each of these polygons. *a)* The image is of geometry figure where three of the sides are labeled, 50°, a and 85°. It is also known that the exterior angle is 110°. *b)* The image is of geometry figure where two of the angles are labeled, 93° and 47°. Find b. *c)* The image is of geometry figure where one of the angles are labeled and equal to 127°. Find c. *d)* The image is of geometry figure where two of the angles are labeled, 115° and 140°. Find d. (4 x 1 = 4 marks) **4** Find the values of the pronumerals in these pairs of congruent triangles. *a)* The image is of 2 congruent triangles, where one of the side lengths is 3 and 4. Find x & y. *b)* The image is of 2 congruent triangles, where one of the angles is 40° and 65°. Find a & b. (2 + 2 = 4 marks) **5** This pair of figures are similar. The image shows two similar pentagons A and B. The sides for pentagon A are 3, y, x, 6. The sides for pentagon B are 6, 6 and 9. *a)* Find a scale factor. *b)* Find the value of x. *c)* Find the value of y. (2 + 1 + 1 = 4 marks) **6** For this pair of triangles: The image shows a triangle and the corresponding side lengths 4, 6, 8 and x. *a)* Give a reason why the two triangles are similar. *b)* Find the value of x. (1 + 2 = 3 marks) **Part C - Extended-response (7 marks)** **1** *a)* Prove that the given pair of triangles is congruent. The image displays of kite. Some key points are labeled A, B, C and D. *b)* Hence, prove that opposite angles in a kite are always equal. (3 + 1 = 4 marks) # **Chapter 7: Geometry Test A answers** **Part A - Multiple-choice** 1. C 2. E 3. D 4. C 5. B 6. D 7. B 8. C 9. D 10. A **Part B - Short-answer** 1. a) $a = 50$ b) $b = 30$ c) $c = 70$ d) $d = 120$ 2. a) $a = 100, b = 100$ b) $c = 64, d = 116$ 3. a) $a = 115$ b) $b = 110$ c) $c = 53$ d) $d = 105$ 4. a) $x = 4, y = 5$ b) $a = 65, b = 75$ 5. a) $\frac{3}{2}$ or 1.5 b) $x = 4.5$ c) $y = 4$ 6. a) AAA b) $x = 18$ **Part C - Extended-response** 1. a) * $BD$ is common * $AB = CB$ (given) * $AD = CD (given)$ $\therefore \Delta ABD = \Delta CBD (SSS)$ $\angle BAD = \angle BCD$ (matching angles in congruent triangles) b) $\angle C$ is common * $\angle CDB = \angle CEA$ (corresponding angles, $AE || BD$) * $\angle CBD = \angle CAE$ (corresponding angles, $AE || BD$) $\therefore \Delta CBD ||| \Delta CAE (AAA)$