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CCGPS Analytic Geometry (8-19-13) UNIT QUESTION: How do I prove geometric theorems involving lines, angles, triangles and parallelograms? Standards: MCC9-12.G.SRT.1-5, MCC9-12.A.CO.6-13 Today’s Question: What does it mean for two triangles to be congruent? Standard: MCC9-12.G.SRT5, CO.7-8 Congruent triangles have congruent sides and congruent angles. The parts of congruent triangles that “match” are called corresponding parts. Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Complete each congruence statement. B A D C F ABC DEF ? E Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? A Complete each congruence statement. B ACB ECD ? C D E Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Complete each congruence statement. T GHK GTK ? G K H Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Corresponding Parts of Congruent Triangles are Congruent Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Fill in the blanks O If CAT DOG, then A ___ CPCTC because ________. O C D G A T Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Fill in the blanks RS If FJH QRS, then JH ___ Q because _______. CPCTC and F ___ If XYZ ABC, then ZX CA ___ and Y B ___ because CPCTC _______. Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean? Overlapping sides are congruent in each triangle by the REFLEXIVE property Vertical Angles are congruent Alt Int Angles are congruent given parallel lines Before we start…let’s get a few things straight C A Y B X INCLUDED ANGLE Z Side-Side-Side (SSS) Congruence Postulate 4 5 6 4 5 6 All Three sides in one triangle are congruent to all three sides in the other triangle Side-Angle-Side (SAS) Congruence Postulate Two sides and the INCLUDED angle Ex 1 Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. R S T ΔRST ΔYZX by SSS Ex 2 In two triangles , DF UV , FE VW and DE UW . Write a congruence statement. DFE UVW SSS by ____ Ex 3 Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. R T S Not congruent. Not enough Information to Tell Ex 4 Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. P R S Q ΔPQS ΔPRS by SAS Ex 5 Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. P S Q U R T ΔPQR ΔSTU by SSS Ex 6 Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. M P R N Q Not congruent. Not enough Information to Tell