If ?ABE is similar to ?ACD by the SAS similarity theorem, AD must equal how many units.

Question

asked Sep 16, 2018 222k views

2 Answers

Anton Bessonov · Answer 1 · 2018-09-22T10:47:38+0000

Answer: 24 units

Explanation:

Given: Δ ABE is similar to Δ ACD by the SAS similarity theorem.

Since the corresponding sides of similar triangles are proportional.

Therefore we have

$(AB)/(AC)=(AE)/(AD)\\\\\Rightarrow(AB)/(AB+BC)=(AE)/(AE+ED)\\\\\Rightarrow(6)/(6+30)=(4)/(AD)\\\\\Rightarrow\ AD=(4*36)/(6)\\\\\Rightarrow\ AD=24$

Hence, if Δ ABE is similar to Δ ACD by the SAS similarity theorem then AD must equal 24 units.