Question

ABCD is a parallelogram. The sides AB, AD are produced to E, F so that AB =BE and AD=DF. prove that the triangles BEC and DCF are congruent

Answer 1

here is the anawer for the question.

Answer 2

Δ BCE is congruent to Δ DFC

Step-by-step explanation:

Given:

ABCD = parallelogram, and

AB= BE,

AD=DF.

solution:

Now,

DC=AB

But AB= BE

So,

DC=BE      .......1

Similarly,

BC=AD

But AD=DF

so, DF= BC      .... 2

Now in Δ BCE and DFC respectively, 2 sides are equal

So, their opposite sides are also equal. therefore, ∠ BCE= ∠ BEC and ∠DCE =∠DCF

Therefore, ∠CBE= ∠FDC...... 3

From equations 1, 2 & 3

Δ BCE is congruent to Δ DFC