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Part I. Fill in the blank. 1. In a triangle, the smallest angle is across from __________________________________________. 2. _____, _____, _____, _____, _____ are the five methods to prove triangles congruent. 4. Equiangular triangles are also ________________________________. 5. Corresponding parts of congruent triangles are _______________________________. 7. The hypotenuse of a right triangle is opposite the ____________________________________. 8. If two sides of a triangle have length 4 and 6 then the third side must be between ____ and ____. Fill in the blank with Always, Sometimes, or Never. 1. Isosceles triangles are acute. _____ 2. An acute triangle is equilateral. _____ 3. A scalene triangle is obtuse. _____ 4. A right triangle is isosceles. _____ Find the value of x. 5. 6. 5x (4x - 3) (7x + 9) 27 34 49 (3x + 56) Determine which postulate or theorem can be used to prove the triangles are congruent. 7. 8. 9. Find the value of x and y. 10. 11. 12. 70 y 4y x x 49 x 24 y 13. What is the vertex of ABC? __________ Write the inequality relating each pair of measures. 1. m PRQ _______ m PRS 2. m DBC ________ m ABE B R 7 Q 15 7 5 P 15 12 9 S 12 A 4 E D 6 C 3. Use the figure to the right to write an inequality to describe the possible values of x. R 10 Q 12 15 (2x - 5) 55 P 15 4. The measures of the angles in a triangle are in the extended ratio 1:4:7. Find the measures of the angles. _____ _____ _____ Solve each proportion. 5 4 5. x3 x 7. Given that ABC Find the geometric mean of the two numbers. 6. 3 and 27 DEF, use the diagram to find the values of x and y. 17. Luke Skywalker is 5 feet 9 inches tall. He casts a shadow that is 3 feet 4 inches long. R2D2 casts a shadow that is 28 inches long. How tall is R2D2? C3PO is 69 inches tall. How long is his shadow? S 8. The dotted segment is a special segment in similar triangles. Find the value of the variable. 14 18 27 z-4 Find the value of the variable. 9. 10. 7 10 12 h g 24 8 12 Part III. Proofs Complete each proof. JK JL 2. GIVEN: K M is the midpoint of KL PROVE: J K L M L Statements Reasons 1. 1. Given 2. M is the midpoint of KL 2. 3. 3. Definition of a midpoint 4. 4. Reflexive property 5. 5. SSS 6. K L 6. Complete the following proof. (not drawn to scale) G GIVEN: 82 GK = 2 GJ = 30 GF = 6 FH = 4 GKF PROVE: K J Statements Reasons 1. 1. Given 2. GJ = 30 2. 3. GF = 6 3. 3. 4. Given 4. GF + FH = GH 5. 6. 6. Substitution Property 7. 7. Combine like terms 2 3 6 10 3 30 2 6 9. 10 30 GK GF 10. GH GJ 11. G ≅ G 12. GKF GHJ F 50 GHJ 8. 48 8. 9. 10. 11. Reflexive Property 12. H