Chapter 3.3, Problem 6PSA

To determine

To show that two angles are congruent.

Answer to Problem 6PSA

  $\angle CODand\angle DOEarecongruent.$

Explanation of Solution

Given information:

In a circle with center O,

  $\overline{CD} \cong \overline{DE}$

Formula used:

The below properties are used:

Radii of a circle are congruent.

Two triangles are congruent by SSS congruence rule.

Proof:

It is given that,

In a circle with center O,

  $\overline{CD} \cong \overline{DE}$

  

Radii of a circle are congruent.

  $\overline{OC} \cong \overline{OE}$

By reflexive property, we get

  $\overline{OD}\cong \overline{OD}$

By SSS congruence rule, we get

  $\Delta COD \cong \Delta EOD$

As corresponding parts of congruent triangles are congruent, we get

  $\angle COD \cong \angle EOD$