Question

Since a parallelogram is defined as a quadrilateral with two pairs of parallel sides, Emily drew in a diagonal of a parallelogram and said that she could prove that the two triangles formed would be congruent using the ASA con- gruence property. How should you respond? g

Answer 1

Explanation:

In the attachment fig ABCD is a parallelogram with AC as diagonal.

we know that,

In  a parallelogram opposite sides are equal and parallel

In a parallelogram sum of adjacent angles is 180°

that is

∠A+∠D= ∠B+∠C= 180°

Also, in  a parallelogram opposite angles are equal.

So in ΔADC and ΔABC

1) AD=BC

2) DC= AB

And

3) ∠ADC= ∠ABC

therefore, ΔADC and ΔABC are congruent to each other and Emily was right.