Question

fill in the missing reason. a. aas b. sas c. sss d. asa

Explanation:

Step1: Recall triangle congruence criteria

• ASA (Angle - Side - Angle): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
• In \(\triangle ABD\) and \(\triangle EBC\):
• We have \(\overline{AB}\cong\overline{BE}\) (given - side).
• \(\angle ABD\cong\angle CBE\) (vertical angles - angle).
• \(\angle A\cong\angle E\) (\(\overline{AD}\parallel\overline{CE}\) gives alternate interior angles - angle).
• The side \(\overline{AB}\) is included between \(\angle A\) and \(\angle ABD\) in \(\triangle ABD\), and the side \(\overline{BE}\) is included between \(\angle E\) and \(\angle CBE\) in \(\triangle EBC\)

Answer:

D. ASA