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Transcript
Name: _____________________________ TP: ____ CRS Objective CW#44H: Apply Congruence and Triangles Honors Geometry PPF 601 – Apply properties of 30-60-90, 45-45-90, similar, and congruent triangles 8.6 Identify corresponding sides and angles of congruent triangles 8.7 Use the Third Angle Theorem to find missing angles in congruent triangles Congruent figures = _________________________________________________________________________ Congruent? Congruent? Congruent? Corresponding parts = _______________________________________________________________________ When you write a congruence statement for two polygons, always list the corresponding vertices in the same _____________________. You can write congruence statements in more than one way, as long as the vertices are listed in the correct order for ______________________. Correct! Correct! PUSH IT TO THE LIMIT. Incorrect! 1) EGI and QMO are congruent 2) TRV and YXZ are congruent List corresponding angles: 1. _____________ 2. _____________ 3. _____________ List corresponding sides: 1. _____________ 2. _____________ 3. _____________ List corresponding angles: 1. _____________ 2. _____________ 3. _____________ List corresponding sides: 1. _____________ 2. _____________ 3. _____________ 3) In the diagram to the below, QRST WXYZ. 4) Given HJK TRS, find the values of a and b. a. Find the value of x. b. Find the value of y. The _______________________________________________________ can be used to solve for missing angles in congruent triangles. It will also lead us to theorems that will help us prove that triangles are congruent. Use the plan below to write a proof for the Third Angles Theorem. PUSH IT TO THE LIMIT. 5) Find the value of y. 6) Find the value of y. What theorem(s) did were used to find the value of y? a) Triangle Sum Theorem b) Exterior Angle Theorem c) Third angles Theorem 7) Use the Third Angles Theorem to find mV. What theorem(s) did were used to find the value of y? a) Triangle Sum Theorem b) Exterior Angle Theorem c) Third angles Theorem SUT VUW by the ________________________________. The diagram shows that STU _________ , so by the Third Angles Theorem, S _________. By the Triangle Sum Theorem, mS = __________________ = _______. So, mS mV = _______ by the definition of congruent angles. 8) Find the value of the indicated angle. 9) Given ABC DEF, find the values of x and y. 10) Find the value of the indicated angle. 11) Find the values of x and y. PUSH IT TO THE LIMIT. Example 5: Prove that triangles are congruent. Given Prove FH JH ,FG JG , FHG JHG, FGH JGH FGH JGH 12. Prove that triangles are congruent. Given Prove E is the midpoint of AC and BD ABE CDE TEXTBOOK 228 – 229: 5 – 14 ODDS ONLY, 15-21, 26 PUSH IT TO THE LIMIT.