Name: 22K 14A 12T /48 MPM1D Unit 7 Review True/False (4K) Indicate whether the statement is true or false. Show your work

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1 Name: _ 22K 14A 12T /48 MPM1D Unit 7 Review 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 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

2 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.

3 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)

4 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)

5 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) Scalene Isosceles Equilateral Acute A B C Obtuse D E F Right G H I a) Draw examples of those that exist. b) Explain why the other cases are impossible using words and diagrams.

6 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 REF: Knowledge and Understanding OBJ: Section 7.4 LOC: MG3.02 TOP: Measurement and Geometry KEY: Midpoint Triangle 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,

7 The measure of each interior angle is 150. PTS: 1 DIF: Level 3 REF: Application OBJ: Section 7.3 LOC: MG3.01 TOP: Measurement and Geometry KEY: Interior angle Polygon 4. ANS: D PTS: 1 DIF: Level 3 REF: Thinking OBJ: Section 7.5 LOC: MG3.02 TOP: Measurement and Geometry KEY: Bisect Quadrilateral 5. ANS: C PTS: 1 DIF: Level 3 REF: Application OBJ: Section 7.5 LOC: MG3.04 TOP: Measurement and Geometry KEY: Kite 6. ANS: A PTS: 1 DIF: Level 3 REF: Application OBJ: Section 7.5 LOC: MG3.04 TOP: Measurement and Geometry KEY: Rectangle 7. ANS: B PTS: 1 DIF: Level 3 REF: Application OBJ: Section 7.5 LOC: MG3.04 TOP: Measurement and Geometry KEY: Rhombus 8. ANS: D PTS: 1 DIF: Level 3 REF: Application OBJ: Section 7.5 LOC: MG3.04 TOP: Measurement and Geometry KEY: Square 9. ANS: D ABCDE is a pentagon. So, if it is regular, then each interior angle, including EDC, measures or 108. Since BAF = 120, and each interior angle of a regular hexagon measures 120, a regular hexagon FABXYZ could be drawn. PTS: 1 DIF: Level 3 REF: Application OBJ: Section 7.3 LOC: MG3.02 TOP: Measurement and Geometry 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.

8 PTS: 1 DIF: Level 3 REF: Application OBJ: Section 7.1 LOC: MG3.01 TOP: Measurement and Geometry KEY: Exterior angle Triangle 2. ANS: The sum of the angles in a triangle is 180. 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 OBJ: Section 7.1 LOC: MG3.01 TOP: Measurement and Geometry KEY: Exterior angle Polygon 4. ANS: The sum of the exterior angles of any quadrilateral is 360. PTS: 1 DIF: Level 3 REF: Application OBJ: Section 7.2 LOC: MG3.01 TOP: Measurement and Geometry KEY: Exterior angle Quadrilateral 5. ANS: The sum of the interior angles in a pentagon is 540.

9 PTS: 1 DIF: Level 3 REF: Application OBJ: Section 7.3 LOC: MG3.01 TOP: Measurement and Geometry 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 REF: Application Thinking OBJ: Section 7.1 LOC: MG3.01 TOP: Measurement and Geometry KEY: Interior angle Triangle

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