Question

Which triangles are similar?

A) ΔABE ∼ ΔACD
B) ΔABE ∼ ΔADC
C) ΔABE ∼ ΔCBE
D) ΔABE ∼ ΔECD

Answer 1

option B) ΔABE ∼ ΔADC

Explanation:

The picture of the question in the attached figure

we know that

If two triangles are similar, then its corresponding sides are proportional and its corresponding angles are congruent

In this problem

Triangles ABE and ADC are similar by AA Similarity Theorem

because

m∠ ABE≅m∠ADC

m∠ BAE≅m∠DAC

The corresponding sides are

AB and AD

BE and DC

AE and AC

so

`(AB)/(AD)=(BE)/(DC)=(AE)/(AC)`