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Honors Geometry Unit #2 Lesson #5 Vertical Angles – nonadjacent angles formed when lines intersect. 2 1 4 1 and 3 are vertical angles. 3 2 and 4 are vertical angles. Theorem: Vertical angles are congruent. Honors Geometry Unit #2 Assignment #5 1. Use the diagram to the right to answer the following questions. a. If m1 = 20°, find m2 and m3. b. If m1 = 110°, find m2 and m3. c. If m1 = 63°, find m2, m3, and m4. d. If m1 = x°, find m1, m2, m3, and m4 in terms of x. 2 1 3 4 2. True or False. If a statement is true, explain why it is true. If a statement is false, provide a counterexample. a. If two angles are vertical then the measure of each angle is 45°. b. If two angles are vertical and supplementary, then they are right. c. If two angles are vertical then the measure of each angle is 90°. 3. Find the measure of each numbered angle below. a. b. 1 123° 2 3 6 7 33° 8 10 9 147° 11 12 60° 13 4 5 4. In the diagram below AE GD , XB bisects AXC, and XH bisects AXG. Find the measure of each of the following angles. A B a. BXC H b. AXD C c. CXD 36° d. GXF e. HXG G f. HXD X g. FXB F h. FXD E 5. Find the measure of each angle in the diagram. 2 1 a. m2 x 20, m4 x 12 5 2 b. m1 20 x 2 72, m4 60 x 28 c. m2 13 x y, m3 10 x y , m4 5 x 3 y 2 1 3 4 D P 6. Use the diagram below to answer the following. a. Name three collinear points. b. Name three noncollinear points. c. Name four coplanar points. d. Name four noncoplanar points. e. Find AB GB . f. Find DE CD . g. Find BD CE h. BA BD i. R CE j. R P R G C D B E A F 7. In the diagram below MN NP , m1 3 x 8 y, m2 3 x 2 y , and m3 6 x 2 y . Find m3. M 2 1 N 3 P 8. In the diagram, m1 = 6x + 21 and m2 = 10x – 25. Are the lines perpendicular? Give an explanation for your answer. 1 2