Warm Up 1. If ∆ABC ∆DEF, then A ? and BC ? . 2. What is the distance between (3, 4) and (– 1, 5)? 3. If 1 2, why is a||b? 4. List the 4 theorems/postulates used to prove two triangles congruent: D EF 17 Converse of Alternate Interior Angles Theorem SSS, SAS, ASA, AAS
EF. 17. Warm Up 1. If ∆ ABC ∆ DEF , then A ? and BC ? . 2. What is the distance between (3, 4) and (–1, 5)? 3. If 1 2, why is a||b ? 4. List the 4 theorems/postulates used to prove two triangles congruent:. D. - PowerPoint PPT Presentation
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Warm Up
1. If ∆ABC ∆DEF, then A ? and BC ? .
2. What is the distance between (3, 4) and (–1, 5)?
3. If 1 2, why is a||b?
4. List the 4 theorems/postulates used to prove two triangles congruent:
Use CPCTC to prove parts of triangles are congruent.
Chapter 4.4 Using Corresponding Parts of
Congruent Triangles
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.
SSS, SAS, ASA, and AAS use corresponding parts to prove triangles congruent. CPCTC uses congruent triangles to prove corresponding parts congruent. This is similar to the converse theorems in Chapter 3.
Remember!
Example 1: Engineering Application
A and B are on the edges of a ravine. What is AB? 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 AB = 18 mi.
Check It Out! Example 1
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.