Chapter Review. In the figure shown, m n and r is a transversal. If m 4 = 112, find the measure of each angle. Explain your reasoning.

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1 In the figure shown, m n and r is a transversal. If m 4 = 112, find the measure of each angle. Explain your reasoning Since 4 and 6 are alternate interior angles, they are congruent. So, m 6 = Since 4 and 2 are vertical angles, they are congruent. So, m 2 = Since 4 and 8 are corresponding angles, they are congruent. So, m 8 = Since 4 and 1 are supplementary angles, the sum of their measures is 180. So, m 1 = A door can swing open 180. The door is open at an angle of 99. What is the measure of the angle between the door and the door jam? The angle between the door and the door jam and the angle that the door is open form a straight line, so they are supplementary angles. The sum of their measures is 180. So, the measure of the angle between the door and the door jam is 81. esolutions Manual - Powered by Cognero Page 1

2 Find the value of x in the triangle. Then classify the triangle by its angles and by its sides. 6. The measure of the angle is 45. Angles: The triangle has all acute angles. Sides: The triangle has no congruent sides. The triangle is an acute scalene triangle. 7. The measure of the angle is 54. Angles: The triangle has all acute angles. Sides: The triangle has two congruent sides. The triangle is an acute isosceles triangle. esolutions Manual - Powered by Cognero Page 2

3 8. The measure of the angle is 45. Angles: The triangle has a right angle. Sides: The triangle has two congruent sides. The triangle is a right isosceles triangle. 9. The measure of the angle is 95. Angles: The triangle has an obtuse angle. Sides: The triangle has no congruent sides. The triangle is an obtuse scalene triangle. 10. Classify the yield sign by its angles and by its sides. The yield sign has three congruent sides and therefore has three congruent angles. Because the sum of the measures of the angles of a triangle is 180, each angle has a measure of three congruent sides. The triangle is an acute equilateral triangle. or 60. So, the triangle has all acute angles and esolutions Manual - Powered by Cognero Page 3

4 Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. If it is not a polygon, explain why. 11. The figure is a polygon because it has 4 sides that only intersect at their endpoints. It is a quadrilateral. It is not a regular polygon because it does not have all sides congruent and all angles congruent. 12. The figure is a polygon because it has 5 sides that only intersect at their endpoints. It is a regular pentagon because it has all sides congruent and all angles congruent. Find the measure of an interior angle of each regular polygon. 13. hexagon Find the sum of the measures of the angles. A hexagon has 6 sides, so n = 6. The sum of the measures of the interior angles is 720. Divide the sum by 6 to find the measure of one angle = 120 So, the measure of one interior angle in a hexagon is gon Find the sum of the measures of the angles. An 18-gon has 18 sides, so n = 18. The sum of the measures of the interior angles is Divide the sum by 18 to find the measure of one angle = 160 So, the measure of one interior angle in an 18-gon is 160. esolutions Manual - Powered by Cognero Page 4

5 15. What is the measure of each interior angle of the stop sign? Find the sum of the measures of the angles. The stop sign has eight sides, so n = 8. The sum of the measures of the interior angles is Divide the sum by 8 to find the measure of one angle = 135 So, the measure of one interior angle of the stop sign is The vertices of figure ABCD are A(1, 3), B(4, 3), C(1, 1), and D( 2, 1). Find the vertices after a reflection over the x-axis. To reflect a point over the x-axis, use the same x-coordinate and multiply the y-coordinate by 1. So, the vertices of the reflection are A (1, 3), B (4, 3), C (1, 1), and D ( 2, 1). esolutions Manual - Powered by Cognero Page 5

6 17. A triangle has vertices N(6, 3), P(3, 9), and Q(9, 6). The triangle is translated 2 units right and two units down. Graph the figure and its image. To find the vertices of the translated triangle. Add 2 to the x-coordinates and subtract 2 from the y-coordinates. The vertices of the translated triangles are N (8, 1), P (5, 7), Q (11, 4). 18. What type of transformation is used when moving up an escalator? A translation is when you slide a figure from one position to another without turning it. So, moving up an escalator is a translation. 19. Triangle ABC has vertices A(2, 0), B(4, 1), and C(1, 3). Graph the figure and its image after a clockwise rotation of 180 about vertex A. Give the coordinates of the vertices for triangle A'B'C'. The coordinates of the vertices of ΔA B C are A (2, 0), B (0, 1), and C (3, 3). esolutions Manual - Powered by Cognero Page 6

7 Graph each figure and its image after a clockwise rotation about the origin. 20. triangle GHJ with vertices G(0, 1), H(3, 3), and J(2, 3); 270 clockwise rotation A 270 degree rotation is the same as three 90 rotations or of a complete circle. The coordinates of the vertices of ΔG H J are G (1, 0), H ( 3, 3), and J (3, 2). 21. quadrilateral NPQR with vertices N(1, 1), P(2, 3), Q(4, 2), and R(4, 2); 90 clockwise rotation The coordinates of the vertices of quadrilateral N P Q R are N (1, 1), P (3, 2), Q (2, 4), and R ( 2, 4). 22. Determine whether the shape of the sign shown has rotational symmetry. If it does, describe the angle of rotation. Yes, the sign has rotational symmetry because it can match itself in three positions. The pattern repeats in 3 even intervals. So, the angle of rotation is or 120. esolutions Manual - Powered by Cognero Page 7