Chapter 3.3, Problem 10PSA

To determine

To show two sides are congruent.

Answer to Problem 10PSA

  $\overline{KM}and\overline{RS}arecongruent.$

Explanation of Solution

Given information:

  $\angle M \cong \angle R,$

  $\angle RPS \cong \angle MOK,$

  $\overline{MP}\cong \overline{RO}$

Formula used:

The below property is used:

Two triangles are congruent by ASA congruence rule.

Proof:

It is given that,

  $\angle M \cong \angle R,$

  $\angle RPS \cong \angle MOK,$

  $\overline{MP}\cong \overline{RO}$

  

By Reflexive property,

  $\overline{PO}\cong \overline{PO}$

By subtraction property,

  $\overline{RP}\cong \overline{MO}$

By ASA congruence rule, we get

  $\Delta KOM \cong \Delta SPR$

As corresponding parts of congruent triangles are congruent, we get

  $\overline{KM} \cong \overline{SR}$