Chapter 4.4, Problem 16WE

To determine

To find: the true statement.

Answer to Problem 16WE

The proof given above concludes that only (1) and (2) statements given in prove are true.

Explanation of Solution

Given information:

Given figure,

Given,

  $\angle S\cong \angle T;\overline{ST}\parallel \overline{QP}$

Given options are,

  $\angle P\cong \angle Q$

  $PR=QR$

$R$ is the midpoint of $\overline{PT}$

Calculation:

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

Given: $\angle S\cong \angle T;\overline{ST}\parallel \overline{QP}$

  $\angle P\cong \angle Q$

  $PR=QR$

$R$ is the midpoint of $\overline{PT}$

Proof:

Statements	Reasons
1. $\angle S\cong \angle T$	Given
2. $\overline{TR}\cong \overline{RS}$	Converse of isosceles theorem
3. $\overline{ST}\parallel \overline{QP}$	Given
4. $\angle Q\cong \angle S;\angle T\cong \angle P$	Alternate interior angles
5. $\angle P\cong \angle Q$	Transitive property
6. $\overline{PR}\cong \overline{QR}$	Converse of isosceles theorem
7. $PR=QR$	Definition of congruent line segments

From the proof given above conclude that only (1) and (2) statements given in prove are true.