Download 22K 14A 12T /48 MPM1D Unit 7 Review

Name: _____________________________________
MPM1D Unit 7 Review
22K
14A
12T
/48
True/False (4K)
Indicate whether the statement is true or false. Show your work
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1. An equilateral triangle always has three 60° interior angles.
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2. A line segment joining the midpoints of two opposite sides of a rectangle bisects the area of the rectangle.
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3. A median of a triangle bisects the area of the triangle.
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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.
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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.
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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.
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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°
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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.
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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
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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.
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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.
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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.
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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