Question

Given to
BE
EC
Prove: AB || DE
A
D
3
C
1
2
E
B
Complete the steps of the proof.

Answer 1

Answer:

Step-by-step explanation:

Given:

$\frac{AD}{DC}=\frac{BE}{EC}$

To Prove:

AB║DE

Solution:

Since, corresponding sides of ΔACB and ΔDCE are proportional,

$\frac{AD}{DC}=\frac{BE}{EC}$

Both the triangles will be similar.

ΔACB ~ ΔDCE [By SAS property of similarity]

Therefore, ∠1 ≅ 2 [CPCTC]

Since, ∠1 and ∠2 are the corresponding angles

Therefore, AB║DE [Converse of corresponding angles theorem]