Question

question 4 of 10
what else would need to be congruent to show that ( \triangle abccong\triangle def ) by sas?
given:
( overline{ab}congoverline{de} )
( overline{ac}congoverline{df} )
a. ( overline{bc}congoverline{ef} )
b. ( overline{ac}congoverline{df} )
c. ( angle ccongangle f )
d. ( angle acongangle d )

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
In \(\triangle ABC\) and \(\triangle DEF\), we are given \(\overline{AB}\cong\overline{DE}\) and \(\overline{AC}\cong\overline{DF}\). The included angle for \(\overline{AB}\) and \(\overline{AC}\) in \(\triangle ABC\) is \(\angle A\), and the included angle for \(\overline{DE}\) and \(\overline{DF}\) in \(\triangle DEF\) is \(\angle D\).

Answer:

D. \(\angle A\cong\angle D\)