Chapter 4.5, Problem 14WE

To determine

To prove: $\overline{RS}\cong \overline{TQ}$

Explanation of Solution

Given information: $\angle R\cong \angle T,\overline{RS}\parallel \overline{TQ}$

Proof:

  

Statements	Reasons
Join $\overline{QS}$	By construction
$\angle R\cong \angle T$	Given
$\overline{RS}\parallel \overline{TQ}$	Given
$\angle RSQ\cong \angle TQS$	If a line intersects two parallel lines then each pair of alternate angles are equal
$\overline{QS}\cong \overline{QS}$	According to reflexive property of congruence, a line segment is congruent to itself
$\Delta RSQ\cong \Delta TQS$	According to ASA congruence criteria, Two triangles are said to be congruent if two angles and the side not included between them of one triangle are congruent to the two angles and the side not included between them of another triangle.
$\overline{RS}\cong \overline{TQ}$	Corresponding parts of congruent triangles are congruent