Question

Justify the last two steps of the proof. Given: MN=PO and MO=PN Prove: MNO=PON

Answer 1

The figure of this problem is attached.

Givens:

• MN=PO and MO=PN.
• NO=NO by hypothesis, because both triangles have NO in common.

Now, according to the hypothesis, all three corresponding sides are congruent, that is:

`MN \cong PO\\MO \cong PN\\NO \cong NO`

Therefore, the SSS postulate, Side-Side-Side postulate, both triangles are congruent. From this congruence each corresponding pair of angles are equivalent.