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Name: _____________________________________ MPM1D Unit 7 Review 22K 14A 12T /48 True/False (4K) Indicate whether the statement is true or false. Show your work ____ 1. An equilateral triangle always has three 60° interior angles. ____ 2. A line segment joining the midpoints of two opposite sides of a rectangle bisects the area of the rectangle. ____ 3. A median of a triangle bisects the area of the triangle. ____ 4. A line segment joining the midpoints of two sides of a triangle bisects the area of the triangle. Multiple Choice (18K) Identify the choice that best completes the statement or answers the question. Show your work. ____ 1. Which of the following statements is true? a. The sum of the exterior angles of a triangle is 360°. b. The exterior angle at each vertex of a triangle is equal to the sum of the interior angles at the other two vertices. c. The sum of the interior and exterior angles at any one vertex of a triangle is 180°. d. All of these. ____ 2. Which of the following is impossible to draw? a. A triangle with three acute interior angles b. A quadrilateral with four 90° exterior angles c. A quadrilateral with four interior acute angles d. None of these. ____ 3. The Canadian 5¢ coin features a beaver design that was first used in 1937. Until 1963, many of these nickels were dodecagons. What was the measure of each interior angle of this regular polygon? a. 30° c. 180° b. 150° d. 1800° ____ 4. Which of the following statements is true? a. The figure that results from joining the midpoints of the sides of a quadrilateral is a parallelogram. b. The diagonals of a rectangle bisect each other. c. The line segment joining the midpoints of two sides of a triangle is half the length of the third side. d. All of these. ____ 5. Which of the following best describes the diagonals of any kite? a. bisect each other c. intersect at 90° b. have the same length d. all of these ____ 6. Which best describes the diagonals of any rectangle? a. They bisect each other. c. They intersect at 90°. b. They bisect each other at 90°. d. All of these. ____ 7. Which best describes the diagonals of any rhombus? a. They bisect each other. c. They have the same length. b. They bisect each other at 90°. d. None of these. ____ 8. Which best describes the diagonals of any square? a. They bisect each other. c. They have the same length. b. They bisect each other at 90°. d. All of these. ____ 9. ABCDE is a polygon with AF drawn as shown. Which statement is correct? a. If the polygon is regular, then interior EDC measures 108°. b. If EAB = 108°, then EAF = 132°. c. If AB = AF, then a regular hexagon FABXYZ could be drawn. d. All of these. Short Answer 1. Find the measures of the unknown angles. (3A) 2. Find the measures of the unknown angles. (3A) 3. Find the measure of the exterior angle, x. (2A) 4. Find the measure of the exterior angle, c. (3A) 5. Find the measure of . (3A) Problem 1. Stephen found a diagram of a pentagon in a book. He wonders if all of the angles can measure 60°. Do you think they can? Justify your reasoning in as many ways as possible. (3T) 2. Some types of triangles named in this table exist, but others do not. (9T) Acute Obtuse Right Scalene A D G Isosceles B E H Equilateral C F I a) Draw examples of those that exist. b) Explain why the other cases are impossible using words and diagrams. MPM1D Unit 7 Review Answer Section TRUE/FALSE 1. ANS: T PTS: 1 DIF: Level 1 REF: Knowledge and Understanding OBJ: Section 7.1 LOC: MG3.01 TOP: Measurement and Geometry KEY: Angle | Equilateral triangle 2. ANS: T PTS: 1 DIF: Level 2 REF: Knowledge and Understanding OBJ: Section 7.5 LOC: MG3.02 TOP: Measurement and Geometry KEY: Midpoint | Bisect 3. ANS: T PTS: 1 DIF: Level 2 REF: Knowledge and Understanding OBJ: Section 7.4 LOC: MG3.02 TOP: Measurement and Geometry KEY: Median | Bisect | Triangle 4. ANS: F A line segment joining the midpoints of two sides of a triangle is parallel to the third side. PTS: 1 DIF: Level 2 OBJ: Section 7.4 LOC: MG3.02 KEY: Midpoint | Triangle REF: Knowledge and Understanding TOP: Measurement and Geometry MULTIPLE CHOICE 1. ANS: D PTS: 1 DIF: Level 3 REF: Knowledge and Understanding OBJ: Section 7.1 LOC: MG3.01 TOP: Measurement and Geometry KEY: Exterior angle | Triangle 2. ANS: C The sum of the interior angles in a quadrilateral is 360°. There cannot be four angles, all measuring less than 90°, since their sum would be less than 360°. PTS: 1 DIF: Level 3 REF: Thinking | Knowledge and Understanding OBJ: Section 7.2 LOC: MG3.01 TOP: Measurement and Geometry KEY: Exterior angle | Interior angle 3. ANS: B A dodecagon has 12 sides. The sum, in degrees, of the interior angles of any polygon is (n – 2)180, where n is the number of sides the polygon has. The measure of each interior angle is then . For a dodecagon, The measure of each interior angle is 150°. 4. 5. 6. 7. 8. 9. PTS: 1 DIF: Level 3 REF: Application OBJ: Section 7.3 LOC: MG3.01 TOP: Measurement and Geometry KEY: Interior angle | Polygon ANS: D PTS: 1 DIF: Level 3 REF: Thinking OBJ: Section 7.5 LOC: MG3.02 TOP: Measurement and Geometry KEY: Bisect | Quadrilateral ANS: C PTS: 1 DIF: Level 3 REF: Application OBJ: Section 7.5 LOC: MG3.04 TOP: Measurement and Geometry KEY: Kite ANS: A PTS: 1 DIF: Level 3 REF: Application OBJ: Section 7.5 LOC: MG3.04 TOP: Measurement and Geometry KEY: Rectangle ANS: B PTS: 1 DIF: Level 3 REF: Application OBJ: Section 7.5 LOC: MG3.04 TOP: Measurement and Geometry KEY: Rhombus ANS: D PTS: 1 DIF: Level 3 REF: Application OBJ: Section 7.5 LOC: MG3.04 TOP: Measurement and Geometry KEY: Square ANS: D ABCDE is a pentagon. So, if it is regular, then each interior angle, including EDC, measures 540° 5 or 108°. Since BAF = 120°, and each interior angle of a regular hexagon measures 120°, a regular hexagon FABXYZ could be drawn. PTS: 1 LOC: MG3.02 DIF: Level 3 REF: Application TOP: Measurement and Geometry OBJ: Section 7.3 KEY: Polygon | Pentagon | Hexagon SHORT ANSWER 1. ANS: Opposite angles are equal, so the unlabelled angle in the triangle measures 40°. The exterior angle at each vertex of a triangle is equal to the sum of the interior angles at the other two vertices. Supplementary angles add to 180°. PTS: 1 DIF: Level 3 REF: Application LOC: MG3.01 TOP: Measurement and Geometry 2. ANS: The sum of the angles in a triangle is 180°. OBJ: Section 7.1 KEY: Exterior angle | Triangle The exterior angle at each vertex of a triangle is equal to the sum of the interior angles at the other two vertices. PTS: 1 DIF: Level 3 REF: Application OBJ: Section 7.1 LOC: MG3.01 TOP: Measurement and Geometry KEY: Exterior angle | Triangle 3. ANS: x and the adjacent interior angle are supplementary, so they add to 180°. All of the interior angles of the triangles measure 60°, because the triangles are equilateral. PTS: 1 DIF: Level 3 REF: Application LOC: MG3.01 TOP: Measurement and Geometry 4. ANS: The sum of the exterior angles of any quadrilateral is 360°. OBJ: Section 7.1 KEY: Exterior angle | Polygon PTS: 1 DIF: Level 3 REF: Application LOC: MG3.01 TOP: Measurement and Geometry 5. ANS: The sum of the interior angles in a pentagon is 540°. OBJ: Section 7.2 KEY: Exterior angle | Quadrilateral PTS: 1 LOC: MG3.01 DIF: Level 3 REF: Application TOP: Measurement and Geometry OBJ: Section 7.3 KEY: Interior angle | Polygon PROBLEM 1. ANS: Consider the pentagon. The interior angles should total 540°. If each triangle interior angle were 60°, then the total for the pentagon would be 10(60°) or 600°. Another argument is as follows. Consider the angles at the centre of the diagram. If each angle were 60°, the five angles would have a sum of 300°, but the total needs to be 360°. PTS: 1 DIF: Level 4 REF: Application | Thinking OBJ: Section 7.3 LOC: MG3.01 | MG3.04 TOP: Measurement and Geometry KEY: Regular polygon | Interior angle 2. ANS: a) Answers will vary. A, B, C, D, E, G, and H are possible. b) F and I are impossible because an equilateral triangle has only 60° angles and so cannot be obtuse or right. PTS: 1 DIF: Level 4 OBJ: Section 7.1 LOC: MG3.01 KEY: Interior angle | Triangle REF: Application | Thinking TOP: Measurement and Geometry