What is ae ? enter your answer in the box. units two segments a d and b c intersect at point e to form two triangles a b e and d c e. side a b is parallel to side d c. a e is labeled 2 x plus 10. e d is labeled x plus 3. a b is 10 units long. d c is 4 units long

The length of AE is 20 units.

Step-by-step explanation:

Given two segments AD and BC intersect at point E to form two triangles ABE and DCE. Side AB is parallel to side DC. A E is labeled 2x+10. ED is labeled x+3. AB is 10 units long and DC is 4 units long.

we have to find the length of AE

AB||CD ⇒ ∠EAB=∠EDC and ∠EBA=∠ECD  

In ΔABE and ΔDCE

∠EAB=∠EDC      (∵Alternate angles)

∠EBA=∠ECD      (∵Alternate angles)

By AA similarity, ΔABE ≈ ΔDCE

therefore,

⇒

⇒

⇒

Hence, AE=2x+10=2(5)+10=20 units

The length of AE is 20 units.