Chapter 4.4, Problem 21WE

To determine

To prove: $\angle 5\cong \angle 6$

Answer to Problem 21WE

Explanation of Solution

Given information:

Given figure,

Given,

$\overline{OP}\cong \overline{OQ}$ ; $\angle 3\cong \angle 4$

Calculation:

The Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite to those sides are congruent.

Converse of Isosceles Theorem: If the two angles of a triangle are congruent, then the sides opposite to those angles are congruent.

Given: $\overline{OP}\cong \overline{OQ}$ ; $\angle 3\cong \angle 4$

Proof: $\angle 5\cong \angle 6$

Statements	Reasons
1. $\overline{OP}\cong \overline{OQ}$	Given
2. $\angle 3\cong \angle 4$	Given
3. $\angle POS\cong \angle QOR$	Vertically opposite angles
$\Delta POS\cong \Delta QOR$	ASA postulate
4. $\overline{OS}\cong \overline{OR}$	Corresponding parts   5. $\cong$ triangles are   6. $\cong$
$\angle 5\cong \angle 6$	Isosceles theorem