Chapter 4.3, Problem 9WE

To determine

To prove: $\angle 3\cong \angle 4$

Explanation of Solution

Given information: $\overline{PQ}\cong \overline{PS},\overline{QR}\cong \overline{SR},\angle 1\cong \angle 2$

Proof:

  

Statements	Reasons
$\overline{PQ}\cong \overline{PS}$	Given
$\overline{QR}\cong \overline{SR}$	Given
$\overline{PR}\cong \overline{PR}$	Reflexive property of congruence (according to reflexive property of congruence, a line segment is congruent to itself)
$\Delta PQR\cong \Delta PSR$	SSS congruence criteria (according to SSS congruence criteria, two triangles are said to be congruent if all sides of one triangle are congruent to the corresponding sides of another triangle)
$\angle 3\cong \angle 4$	Corresponding parts of congruent triangles are congruent

In the above proof, the information $\angle 1\cong \angle 2$ is not required.