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Triangles Student Module 1. Classify each triangle by its angles and sides. a. b. 8 8 51 7 7 8 2. c. 9.9 35 27 Name a complementary pair of angles and a supplementary pair of angles in the figure below. C D 40 50 A B 3. E Refer to the figure to answer the following questions. a. Name a pair of vertical angles. b. Can you assume that YUW and WUV are supplementary from the figure? Explain. c. Which angle is complementary to YWT? d. Identify a pair of angles that are congruent. e. Are YWU and UWZ: i. congruent? iv. complementary? ii. adjacent? v. supplementary? iii. vertical? vi. a linear pair? X V T Y U W Z 4. Refer to the figure to answer the following questions. a. Can you determine that SRP and PRT are complementary from the figure? Explain. b. Name two angles that are adjacent, but not complementary or supplementary. c. Given that Q and QPS are supplementary, is Q obtuse, acute, or right? P Q T R S 5. Find the value of x for each figure. a. b. (x+4) (2x) (2x) (3x) 6. Find the measure of angle A. A a. (3x) A b. 104 41 65 B 135 C D G F 7. Given ∆ ABC ∆ PHL, complete the following statements: a. P 60 b. BC c. m L = L B P 25 32 45 75 A 28 C H d. AC = e. ∆ HPL 8. Determine whether each pair of triangles is congruent. If yes, explain why. a. ∆DGF ∆ b. D DG FE GF ED E G F X W WP YP ZP XP P ∆ XPY ∆ Y Z c. B C E F AF DE ∆ABE ∆ A B C F E D J d. GJ IJ GI ∆ GJH ∆ G H I 9. On the graph, draw a triangle and label the coordinates of the vertices. Find the midpoint of two of the sides and draw a segment connecting them. There is a geometric theorem that says that the measure of this segment is equal to half of the measure of the third side. Prove this theorem algebraically. 10. The coordinate grids below show three paths to get from point A(-3,-1) to point B(2,2). a. b. Path 1 Find the distance along each path. Round to hundredths. If the grid represents streets in a city, which path would a taxicab be least likely to take? Explain your reasoning. Path 2 Path 3 11. Given ∆ DAR with vertices D(2,6), A(4,-5), and R(-3,0), use the distance formula to show that ∆ DAR is scalene. 12. Tom and Joe are going hiking. Tom hikes from the parking lot to Horse Rock, and Joe stays at the Parking Lot. a. Both hikers have portable radios that have a maximum range of two miles. Can Tom and Joe get in contact with each other when Tom reaches Horse Rock? Explain your answer. b. Later that day Joe starts hiking and meets Tom for lunch at the halfway point between the parking lot and Horse Rock. What are the coordinates of their grid location for lunch? Show your work. 13. A baseball diamond is a square with 90-foot sides. What is the approximate distance of a catcher’s throw from home plate to second base? 14. The following is a rule of thumb for safely positioning a ladder: The distance from the bottom of the ladder to the wall should be onefourth of the length of the ladder. Thus, the bottom of a 16-foot ladder should be 4 feet from the wall. How far up the wall will the ladder reach? 15. Which of the following best describes the triangle? 7 5 9 a. c. 16. b. d. equilateral right Angles 1 and 2 are supplementary. If m1 is 67, what is the measure of 2? a. c. 17. scalene isosceles 67 113 Find the measure of 1. a. 32 c. 35 b. d. b. d. 23 123 58 55 32 35 1 18. In which of the following figures are 1 and 2 vertical angles? a. b. 2 1 c. 1 d. 1 In which of the following figures are 1 and 2 a linear pair? a. b. c. 1 2 1 d. 1 2 20. 1 2 2 19. 2 2 1 2 In which of the following figures are 1 and 2 complementary angles? a. b. 1 1 2 c. d. 1 2 1 2 2 21. In which of the following figures are 1 and 2 supplementary angles? a. b. 1 c. 2 1 d. 1 1 2 2 22. 2 Given ∆ABC and ∆ADC with AB AD and BAC DAC, determine which postulate can be used to verify that ∆ABC ∆ADC. B A C D a. c. ASA SSS b. d. SAS SSA