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1. In the figure below, m<B = 40o, m<X = 60o, and m<Z = 80o. What reason could prove that ABC and XYZ are similar? 2. 3. If <A = <X and <B = <Y, a. What reasons could prove the two triangles are congruent? b. What reasons would NOT prove the two triangles are congruent? 4. Name all pairs of consecutive interior angles. 5. A ladder is leaning against a house, which is 20 feet tall. What is the approximate length of the ladder to the nearest foot? 6. What is the measure of side PQ to the nearest tenth? 7. Triangle ABC is a right triangle. The measure of angle A is 30o. What is the length of side AC? 8. List the angles from least to greatest. 9. List the angles from largest to smallest 21. Which lists the sides of 10. List the sides from largest to smallest.DBCD in order from 11. List the sides to from shortest to longest. shortest longest? A B C D CD, BC, BD, BC, BD, CD, CD , BD , BC BD BC CD 22 G0921B2-Triangles & Logic 12. Given two sides of a triangle measure 14 inches and 8 inches. Select the three lengths that could be the measure of the third side. 3 inches 6 inches 10 inches 13 inches 15.5 inches 22 inches 25 inches 13. The side lengths of a triangle are 20 and 35. Which could NOT be the length of the third side? 16 40 50 55 14. Circle all of the following that could be the lengths of the sides of a triangle. 3, 5, 7 2, 2, 4 6, 10, 2 7, 4, 5 5, 10, 4 15. 16. What is the inverse of the conditional statement? Determine whether the inverse is true or false. If it is false, find a counterexample. People who live in Texas live in the United States. A People who live in the United States live in Texas. False; they could live in Oklahoma. B People who do not live in the United States do not live in Texas. True C People who do not live in Texas do not live in the United States. False; they could live in Oklahoma. D People who do not live in Texas live in the United States. True 17. Find the value of x. Then find the length of AE. x = ___________________________ AE = ___________________________ 18. Which of the following correctly describes the relationship between the sides of the triangles below? AE AB AB AE AB AE ED EC CD EC CD ED 19.. In this figure, AC and BD bisect each other. Based on the information given, which triangle congruence theorem could be used to prove AED = CEB? A. B. C. D. AAS ASA SAS SSS 20. IF MNO = PQR, which of the following can you NOT conclude as being true? (DRAW A PICTURE!) DRAW PICTURE HERE: 21. 23. Can 15, 10 and 10 be the lengths of the sides of a right triangle? Explain. 24. Complete the reasons in the following proof: Reasons: Given Def. of Midpoint CPCTC Def. of Bisector Vertical Angles Reflexive Property Alternate Interior Angles SSS-SAS-ASA-AAS Statements Reasons ̅̅̅̅ ̅̅̅̅ ≅ 𝑄𝐾 1) 𝑃𝐾 1) ________________________________ 2) ̅̅̅̅ 𝐾𝐿 bisects PKQ 2) ________________________________ 3) PKL QKL 3) ________________________________ 4) ̅̅̅̅ 𝐾𝐿 ≅ ̅̅̅̅ 𝐾𝐿 4) ________________________________ 5) PKL QKL 5) ________________________________ 6) <P = <Q 6) ________________________________ 25. Name whether the triangles are congruent by SSS, SAS, ASA, AAS or if they are not congruent _________________________ _________________________ _________________________ ________________________ 26. If the coordinates of A are (6, 2) and the midpoint of AB is (3, 1) then what are the coordinates of B? 27. The lengths of two sides of DABC are 30 in. and 44 in. Which of the following could NOT be the length of the third side? Select all values. 14 15 36 74 79 28. Order the sides of triangle QRS from shortest to longest. 29. Line m contains points (1, -3) and (2, 2). Which of the following pairs of points define a line parallel to line m? (-4, 0) and (5, 5) (1, 1) and (6, 2) (0, 0) and (1, 5) (0,0) and (-1, 1)