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

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

$<WVX\cong<TVU$
Vertical Angles Theorem

The triangles cannot be proven congruent

$<TRS\cong<URV$

$<RST\cong<RUV$

$\overline{TS}\cong\overline{VR}$

$\overline{TR}\cong\overline{RU}$

 $<JLK\cong<MLN$ 

 $<LKJ\cong<LMN$ 

 $\overline{JL}\cong\overline{MN}$ 

 $\overline{KL}\cong\overline{LM}$ 

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
$\overline{AC}\cong\overline{AB}$

Congruent by SAS
$<BAC\cong<BDC$

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

Congruent by AAS
$<BAC\cong<BDC$

Congruent by AAS
$<BCD\cong<DCA$

2

5

7

12

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

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

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

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