Question

congruent triangles (topic 5)
what reason shows that △ace≅△bcd?
o asa
o sas
o hl
o aas

Explanation:

Step1: Identify equal elements

We see that $\angle ACE=\angle BCD$ (vertically - opposite angles). Also, $AC = BC$ and $CE=CD$ (marked equal in the figure).

Step2: Recall congruence criteria

The Side - Angle - Side (SAS) congruence criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent. Here, in $\triangle ACE$ and $\triangle BCD$, we have two sides ($AC = BC$ and $CE = CD$) and the included angle between them ($\angle ACE=\angle BCD$).

Answer:

B. SAS