Geometry Chapter 7

• Chapter 7 focuses on geometry
• This is a test worth 40 marks divided into 3 parts: multiple choice, short answer and extended response

Part A - Multiple Choice:

• Question 1: Asks for the complementary angles, which are 2 angles adding up to 90°, therefore the answer is the pair 27° and 63°
• Question 2: Triangle with two equal sides and one angle is 40°, so has to be an acute isosceles triangle
• Question 3: Diagram shows two lines cut by transversal with angles 115° and 75°. The lines are not parallel and cointerior angles are not supplementary
• Question 4: Diagram shows two parallel lines cut by a transversal.
• The angle ABC, using corresponding angles, is equal to 64°
• Question 5: Requires a definition of a quadrilateral.
• A rhombus is a quadrilateral that has two pairs of parallel sides and whose sides are all of an equal length
• Question 6: Requires you deduct the value of x in a hexagon. As all exterior angles add up to 360 degrees. x = 60°
• Questions 7 and 8: Asks to select which congruence test proves the triangles are congruent. Requires recall of triangle similarity tests AAA, SSS etc.
• Question 7: The answer is Side Angle Side (SAS)
• Question 8: The answer is Side Side Side (SSS)
• Question 9: Requires which similarity test proves triangles are similar and the answer is Angle Angle Angle tests.
• Question 10: Gareth wishes to determine the width of the river and places markers as shown. Using similar triangles, the width of the river is 24 m

Part 2 - Short Answer

Question 1: Find value of each pronumeral

• (a) with angle 40° will be 50° as one angle is 90°
• (b) with angle 120° will be 30° as one angle is 30°
• (c) using the angles 65° and 45° it will be 70° as supplementary angle.
• (d) with equivalent angles 60° will be 120° for d because triangle adds up to 180°

Question 2: Requires finding the value of each pronumeral and giving a reason

• (a) When one straight line cuts two parallel lines, cointerior angles are supplementary, a = 100
• (b) When one straight line cuts two parallel lines, cointerior angles are supplementary, c = 64, d = 116

Question 3: Requires find the value of the pronumeral in each of these polygons.

• (a) Using angles 50°, 85° and 110°. a = 115°
• (b) Using angles 93° and 47°. b = 110°
• (c) Using an area of 127°, the angle c = 53° because quadrilateral adds up to 360°
• (d) Using angles of 115° and 140°. d = 105°

Question 4: Find the values of the numerals in these pairs of congruent triangles

• The value of x = 4, and y = 5
• In the other triangle, a = 65 degrees, b = 75 degrees

Question 5: This pair of figures are similar.

• To find the value of the scale factor, divide 3 by 2
• Value of x = 4.5
• Value of y = 4

Question 6 : For this pair of triangles:

• To show the triangles are similar, the answer is AAA (Angle Angle Angle)
• Value of x is 18

Part 3 - Extended response

Question 1:

• To prove that the given pair of triangles is congruent it can be shown that BD is common, AB = CB, AD = CD
• Therefore AABD = ACBD
• Therefore ∠BAD = ∠BCD

Question 2:

• Hence, to prove that opposite angles in that the kite are always equal it is proven that ∠C is common
• ∠CDB = ∠CEA
• ∠CBD = ∠CAE
• Triangle CBD is similar to triangle CAE by AAA

This test focuses on geometrical concepts. It includes questions about complementary angles, types of triangles, parallel lines and transversals, quadrilaterals and exterior angles.