5.7 Using Congruent Triangles

​Chapter 5

Congruent Triangles

Section 5.7

Using Congruent Triangles

Corresponding Parts

CPCTC

Congruent triangles have congruent corresponding parts. So, if you can prove that two triangles are congruent, then you know that their corresponding parts must be congruent as well.

CPCTC = Corresponding Parts of Congruent Triangles are Congruent

Explain how you can use the given information to prove that the hang glider parts are congruent.

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Example 1

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Multiple Choice

All three pairs of sides are congruent. Which shortcut is used to prove the triangles congruent?

• SAS

• SSS

• ASA

• AAS

Multiple Choice

Complete the statement:

$$\Delta ABD\cong$$ _______

• $$\Delta CBD$$

• $$\Delta BCD$$

• $$\Delta DCB$$

Multiple Choice

We now know that the two triangles are congruent. How do we know that $$\angle A\cong\angle C$$ ?

• Vertical Angles

• Alternate Interior Angles

• CPCTC

Use the following method to find the
distance across the river, from point N
to point P.

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​Example 2: Using Congruent Triangles for Measurement

​Example 3: Planning a Proof Involving Pairs of Triangles

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Multiple Choice

Which shortcut would we use to prove $$\Delta QSP\cong\Delta TRU$$ congruent?

• SAS

• SSS

• ASA

• HL

Multiple Choice

Which shortcut would we use to prove $$\Delta PRT\cong\Delta USQ$$ congruent?

• SAS

• SSS

• ASA

• AAS

Multiple Choice

How do we know that $$\overline{PT}\cong\overline{UQ}$$ ?

• Reflexive Property

• SSS

• CPCTC

• $$\overline{PT}\ \parallel\ \overline{UQ}$$

Multiple Choice

Which shortcut would we use to prove $$\Delta PTU\cong\Delta UQP$$ congruent?

• SAS

• SSS

• ASA

• HL