Question

The figure shows two parallel lines AB and DE cut by the transversals AE and BD:

Which statement best explains the relationship between Triangle ABC and Triangle EDC ?

Answer 1

Answer:
`\triangle ABC\sim \triangle EDC`

That is, triangles ABC and EDC are similar.

Explanation:

Given :
`AB\parallel DE`

AE and BD are the common transversal of the parallel lines AB and DE,

Then By the alternative interior angle theorem,

`\angle BAC\cong \angle DEC`

And,
`\angle ABC\cong \angle EDC`

Thus, By AA similarity postulate,

`\triangle ABC\sim \triangle EDC`

⇒ triangles ABC and EDC are similar.