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CCGPS Analytic Geometry (8-19-13)

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.

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CCGPS Analytic Geometry (8-19-13)

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  1. 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

  2. Congruent Triangles 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?

  3. Complete each congruence statement. B A C D F DEF E Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

  4. Complete each congruence statement. B A C E D ECD Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

  5. Complete each congruence statement. T G K H GTK Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

  6. CPCTC CorrespondingParts of CongruentTriangles are Congruent Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

  7. O C D G T A Fill in the blanks O If CAT  DOG, then A  ___ because ________. CPCTC Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

  8. If XYZ  ABC, then ___ and Y  ___ because _______. Fill in the blanks If FJH  QRS, then ___ and F  ___ because _______. Q CPCTC CPCTC B Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

  9. Proving Triangles Congruent Essential Question: What does it mean for two triangles to be congruent and what does CPCTC mean?

  10. Overlapping sides are congruent in each triangle by the REFLEXIVE property Alt Int Angles are congruent given parallel lines Vertical Angles are congruent

  11. C Y A B X Z Before we start…let’s get a few things straight INCLUDED ANGLE

  12. Side-Side-Side (SSS) Congruence Postulate 4 4 5 5 6 6 All Three sides in one triangle are congruent to all three sides in the other triangle

  13. Side-Angle-Side (SAS) Congruence Postulate Two sides and the INCLUDED angle

  14. Ex 1 R S Y X T Z Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. ΔRST ΔYZX by SSS

  15. Ex 2 DFE UVW by ____ SSS

  16. Ex 3 R B C A T S Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. Not congruent. Not enough Information to Tell

  17. Ex 4 Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. P R Q S ΔPQSΔPRS by SAS

  18. Ex 5 Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. P S U Q R T ΔPQRΔSTU by SSS

  19. Ex 6 Determine whether the triangles are congruent. If they are, write a congruency statement explaining why they are congruent. M P R Q N Not congruent. Not enough Information to Tell

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