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Geometry Unit 3 Review Sheet Name: _____________________________ I can prove that triangles are congruent using valid theorems/postulates. (G-CO.8) 1. What congruence shortcuts can you use to prove that triangles are congruent? List all 5 of the methods. 2. For each of the following triangles, determine which theorem/postulate could be used to show that the triangles are congruent. If they are congruent, write a congruence statement, if there is not enough information, explain why you cannot prove the triangle congruent. Triangles: Are these triangles If the triangles are congruent, Don’t forget to mark additional sides/angles which Congruent? By write a congruence statement. are congruent! which theorem or If the triangles are NOT postulate? congruent, explain why they are not congruent. I can prove that triangles are congruent using valid theorems/postulates. (G-CO.8) 3. Suppose PQ AB and QS BC . What is needed to prove PQS ABC by each method? Draw two triangles representing this situation. What additional information is needed to prove congruent by SSS? We would need What additional information is needed to prove congruent by SAS? We would need 4. Complete the following proof. Statements Justifications 1. 1. Given 2. 4. 2. Alternate interior angles are congruent. 3. Alternate interior angles are congruent. 4. Given 5. ABC EDC 5. 3. I can use the definition of congruent triangles and corresponding parts to solve problems. (G-CO.7) 5. Given that LMN PQR, complete the following congruence statements: L _____ MN ____ R _____ PR ____ 6. In an isosceles triangle PQR, PQ QR , the measure of the vertex angle is (4x + 10) The measure of each base angle is (2x - 5). a. Draw an isosceles triangle and label each angle with the given information b. Write an equation and solve for x. c. Find the measure of each base angle. d) Find the measure of the vertex angle. 7. Given: NEW YAR . Let mE (14 x 4) , mY (3x 7) and mW 75 Draw and label both triangles to the right. List all six pairs of corresponding congruent parts Write an equation to solve for x. I can prove theorems about triangles and use these theorems to solve problems.(G-CO.10) 8. Complete the proof. Given: A C ; BD bisects ABC Statements 1. Justifications Given 2. Given 3. Definition of angle bisector 4. All right angles are congruent Prove: ABD CBD B A D C 5. ABD CBD I can prove theorems about triangles and use these theorems to solve problems.(G-CO.10) 9. Find all the missing angle measures in the diagram shown. ma=_______ mh=_______ mb=_______ mk=_______ mc=_______ mm=_______ md=_______ mp=_______ me=_______ mr=_______ mf=_______ ms=_______ mg=_______ mb=___________ mc=___________ md=___________ me=___________