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Lesson 4–6 Objectives

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Lesson 4–6 Objectives - PowerPoint PPT Presentation


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Lesson 4–6 Objectives. Be able to use CPCTC to prove parts of triangles congruent. CPCTC is an abbreviation for the phrase “ C orresponding P arts of C ongruent T riangles are C ongruent.” It can be used as a justification in a proof AFTER you have proven two triangles congruent.

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Presentation Transcript
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Lesson 4–6 Objectives

  • Be able to use CPCTC to prove parts of triangles congruent
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CPCTC is an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent.”

It can be used as a justification in a proof AFTER you have proven two triangles congruent.

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Remember!

SSS, SAS, ASA, AAS, and HL use corresponding parts to prove triangles congruent.

CPCTC uses congruent triangles to prove corresponding parts congruent.

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Applying CPCTC

A landscape architect sets up the triangles shown in the figure to find the distance JK across a pond.

What is JK?

One angle pair is congruent, because they are vertical angles.

Two pairs of sides are congruent, because their lengths are equal.Therefore the two triangles are congruent by SAS. By CPCTC, the third side pair is congruent, so JK = 41 ft.

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Z

Proving Corr. Parts 

Given:YW bisects XZ, XY YZ.

Prove:XYW  ZYW

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Using CPCTC in proofs

Given:NO || MP, NP

Prove:MN || OP

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Using CPCTC in proofs

Given: J is the midpt of KM & NL

Prove:KL || MN

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