Question

explain how the diagonal of a parallelogram divide it into two congruent triangles. STEP BY STEP EXPLANATION

Answer 1

Let ABCD a parallelogram.

Construction: Join BD

AB is parallel to CD.

BC is parallel to DA.

So,angle ABD = angle CDB -1

angle ADB = angle CBD -2

(Alternate interior angle are equal)

In ∆ABD and ∆ BCD

(A) angle ABD = angle CDB -(by eq 1 )

(S) BD = BD - (common side)

(A) angle ADB = angle CBD - (by eq 2 )

Therefore,∆ABD = ∆BCD - by ASA similarity creation

Hence prove....

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