# Module 3 - Unit 3: Pythagoras' Theorem

## Self-Audit

For the multiple choice questions below, choose one answer, (a), (b), (c) or (d), that is CORRECT by clicking the appropriate box.
Calculators are NOT allowed unless it is indicated in the question.

## Section 3.1 - Pythagoras' Theorem

Question 1
 Which side is the HYPOTENUSE in the diagram below? (A) XY   (B) YZ (C) XZ (D) None of these
Question 2
 Which side is the HYPOTENUSE in the diagram below? (A) XY   (B) YZ (C) XZ (D) None of these
Question 3
 Which of the following sets of numbers are Pythagorean triples (that is, a2 + b2 = c2)?     1.  3, 4, 5     2.  5, 6, 7     3.  6, 8, 10 (A) 1 only   (B) 1 and 2 only (C) 1 and 3 only (D) 2 and 3 only
Question 4
 What value of x satisfies x2 = 92 + 122? (A) 15   (B) 18 (C) 21 (D) None of these

## Section 3.2 - Calculating the Length of the Hypotenuse

Question 5
 What is the length of the hypotenuse in the triangle below? (A) 13 cm   (B) 15 cm (C) 17 cm (D) None of these
Question 6
 What is the length of the hypotenuse in the triangle below? Give your answer correct to 1 decimal place. (A) 8.0 cm   (B) 9.2 cm (C) 9.3 cm (D) 10.0 cm
Question 7
 What is the length of the diagonals of a square of side 6 cm? Give your answer correct to 1 decimal place. (A) 8.4 cm   (B) 8.5 cm (C) 8.6 cm (D) 12.0 cm
Question 8
 What is the length of the diagonal of the rectangle below? Give your answer correct to 1 decimal place. (A) 10.0 cm   (B) 5.0 cm (C) 3.6 cm (D) 3.5 cm

## Section 3.3 - Calculating the Lengths of Other Sides

Question 9
 What is the length of the side marked x in the triangle below? Give your answers correct to 1 decimal place. (A) 13.2 cm   (B) 13.3 cm (C) 25.0 cm (D) None of these
Question 10
 What is the length of the side marked x in the triangle below? Give your answers correct to 1 decimal place. (A) 3.0 cm   (B) 7.9 cm (C) 9.0 cm (D) None of these
Question 11
 What is the perpendicular height of the isosceles triangle shown below? Give your answer correct to 1 decimal place. (A) 6.5 cm   (B) 6.6 cm (C) 6.7 cm (D) 7.4 cm
Question 12
 What is the perpendicular height of an equilateral triangle with sides of length 6 cm? Give your answer to 1 decimal place. (A) 5.1 cm   (B) 5.2 cm (C) 5.5 cm (D) 6.7 cm

## Section 3.4 - Problems in Context

Question 13
 A ship sails 200 km due east and then 100 km due north. At the end of this journey, how far is the ship from its starting position? Give your answer to the nearest 10 km. (A) 170 km   (B) 200 km (C) 220 km (D) None of these
Question 14
 What is the area of the triangle shown below? (A) 42 cm2   (B) 67.5 cm2 (C) 84 cm2 (D) None of these
Question 15
 What is the perimeter of the triangle shown below? (A) 30 cm   (B) 34 cm (C) 60 cm (D) None of these
Question 16
 What is the perimeter of the parallelogram shown below? Give your answer to the nearest millimetre. (A) 20.0 cm   (B) 20.9 cm (C) 21.0 cm (D) None of these Mark your answers.