#5.7 Using Congruent Triangles

Fill in the blank:

Corresponding Parts of Congruent Triangles are ___________________.

• Corresponding

• Congruent

• Complete

• Coordinating

Planning a Proof:

What could you use to prove the triangles are congruent?

• $<TUV\cong<WXV$
  Alternate Interior Angles Theorem

• $\overline{UV}\cong\overline{VX}$
  Segment Bisector Theorem

• $<WVX\cong<TVU$
  Vertical Angles Theorem

• The triangles cannot be proven congruent

The pair of triangles shown are congruent by the Hypotenuse-Leg Theorem. Which statement is true?

• $<TRS\cong<URV$

• $<RST\cong<RUV$

• $\overline{TS}\cong\overline{VR}$

• $\overline{TR}\cong\overline{RU}$

The pair of triangles shown are congruent by the SAS Congruence Theorem. Which statement is true?

•  $<JLK\cong<MLN$ 

•  $<LKJ\cong<LMN$ 

•  $\overline{JL}\cong\overline{MN}$ 

•  $\overline{KL}\cong\overline{LM}$ 

The pair of triangles are congruent.

Name the theorem that proves this and a pair of congruent parts.

• Congruent by AAS
  $\overline{AC}\cong\overline{AB}$
  

• Congruent by ASA.
  $\overline{EB}\cong\overline{AC}$
  

• Congruent by AAS.
  $\overline{EB}\cong\overline{AC}$
  

• Congruent by ASA
  $\overline{AC}\cong\overline{AB}$
  

The pair of triangles are congruent.

Name the theorem that proves this and a pair of congruent parts.

• Congruent by SAS
  $<BAC\cong<BDC$
  

• Congruent by SAS.
  $<BCD\cong<DCA$
  

• Congruent by AAS
  $<BAC\cong<BDC$
  

• Congruent by AAS
  $<BCD\cong<DCA$
  

Find DE

• 2

• 5

• 7

• 12

Why is $\Delta WXV\cong\Delta YXZ$   ?

• Because of the vertical angles theorem and AAS

• Because of the vertical angles theorem and SAS

• Because of the alternate interior angles theorem and AAS

• Because of the alternate interior angles theorem and SAS

Why is $\Delta IGK\cong\Delta HJK$   ?

• Because of the vertical angles theorem and AAS

• Because of the vertical angles theorem and SAS

• Because of the alternate interior angles theorem and AAS

• Because of the alternate interior angles theorem and SAS

Choose the correct PLAN to prove that
 $<H\cong<J$  

•  $<HIK\cong<JIK$  
   $\Delta IHK\cong\Delta IJK$  
   $<H\cong<J$  
  

•  $\overline{IK}\cong\overline{IK}$ 
   $\Delta IHK\cong\Delta IJK$  
   $<H\cong<J$