Chapter 3.3, Problem 3PSA

To determine

To show that two sides are congruent.

Answer to Problem 3PSA

  $\overline{MR}and\overline{PR}arecongruent.$

Explanation of Solution

Given information:

In a circle with center O,

  $RO\perp MP$

Formula used:

The below properties are used:

If two segments are perpendicular, they form right angles.

Right angles are congruent.

Two triangles are congruent by SAS congruence rule.

Proof:

  

We know that radii of circle are congruent.

  $\overline{OM} \cong \overline{OP}$

It is given that,

  $RO\perp MP$

If two segments are perpendicular, they form right angles.

  $\angle MORisarightangle.$

  $\angle PORisarightangle.$

Right angles are congruent.

  $\angle MOR\cong \angle POR$

By reflexive property, we get

  $\overline{RO}\cong \overline{RO}$

By SAS congruence rule, we get

  $\Delta MRO\cong \Delta PRO$

As corresponding parts of congruent triangles are congruent, we get

  $\overline{MR}\cong \overline{PR}$