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Mastering Congruent Triangles: The CPCTC Approach

Learn how to prove triangles congruent using CPCTC and discover the key principles involved, such as SAS, AAS, and SSS. Practice finding unknowns in congruent triangles and explore the Reflexive Property. Class activities and explanations are provided in an interactive manner.

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Mastering Congruent Triangles: The CPCTC Approach

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  1. Bell Work • List the five ways to prove two triangles congruent. • Complete each sentence below: • Class starts when the _______________. • We do not _____________when the teacher is talking. • ___________________are to be treated with respect.

  2. L _____ _____ J N K M Lets use CPCTC! Objective: Be able to use CPCTC to find unknowns in congruent triangles! What do you think? Are these triangles congruent? By which postulate/theorem? Oh, and what is the Reflexive Property again? It says something is equal to itself. EX

  3. We learn by doing, and in the process you're going to fall on your face a few times... though I didn't think you'd take it quite that literally.

  4. C.P.C.T.C. Corresponding Parts of Congruent Triangles are CONGRUENT!! C.P.C.T.C. Once you have shown triangles are congruent, then you can make some CONCLUSIONS about all of the corresponding parts (_______ and __________) of those triangles! sides angles

  5. B Y Z C X A Are the triangles congruent? By which postulate or theorem? Yes; ASA What other parts of the triangles are congruent by CPCTC? If <B= 3x and ,Y = 5x –9, find x. 3x = 5x - 9 9 = 2x

  6. C L 3 4 1 2 R S It’s time to do a proof! Given: Prove: Given 2. _______________ 2. Reflexive SAS CPCTC 4. _______________ 4. ___________

  7. C V Given: R H A E Prove: 1. _____________________ 1. Given 2. _____________________ 2. SSS CPCTC 3. _____________________ 3. ________

  8. R C Q Y P T State why the two triangles are congruent and write the congruence statement. Also list the other pairs of parts that are congruent by CPCTC. AAS

  9. 40 yd 30 yd 24.5 yd 30 yd 40 yd A geometry class is trying to find the distance across a small lake. The distances they measured are shown in the diagram. Explain how to use their measurements to find the distance across the lake. Vertical angles are congruent. The triangles are congruent by SAS. The width of the lake has to be 24.5 yd by CPCTC.

  10. http://www.authorstream.com/Presentation/mrfollett-106463-review-triangle-congruence-geometry-math-basketball-education-ppt-powerpoint/http://www.authorstream.com/Presentation/mrfollett-106463-review-triangle-congruence-geometry-math-basketball-education-ppt-powerpoint/

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