Question

the proof ( \triangle abc cong \triangle dcb ) that is shown.
given: ( angle a cong angle d ); ( overline{cd}||overline{ab} )
prove: ( \triangle abc cong \triangle dcb )
what is the missing reason in the proof?

statement	reason
2. ( overline{cd}		overline{ab} )	2. given
3. ( overline{cb} cong overline{bc} )	3. refl. prop.
4. ( angle abc cong angle dcb )	4. alt. int. ( angle s ) are ( cong )
5. ( \triangle abc cong \triangle dcb )	5. ?

• alt. ext. ( angle s ) are ( cong )
• asa
• aas
• corr. int. ( angle s ) are ( cong )

Explanation:

• In the proof, we have two angles (\(\angle A\cong\angle D\) and \(\angle ABC\cong\angle DCB\)) and a non - included side (\(\overline{CB}\cong\overline{BC}\)).
• The AAS (Angle - Angle - Side) congruence criterion states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.

Answer:

AAS