Chapter 5.6, Problem 7PSA

a.

To determine

To find:VWTU is an isosceles trapezoid.

Answer to Problem 7PSA

Yes, VWTU is an isosceles trapezoid.

Explanation of Solution

Given information:

RSTUis a square,

  $\overline{VR}\cong \overline{SW}$

  

  $\overline{UT }\parallel \overline{RS }$

  $\angle URV$ and $\angle TSW$ are right angles.

Two triangles are congruent by SAS congruence rule.

  $\Delta URV\cong \Delta TSW$

Corresponding parts of congruent triangles are congruent.

  $\overline{UV}\cong \overline{TW}$

VWTU is an isosceles trapezoid.

b.

To determine

To find:TriangleVWX is an isosceles triangle.

Answer to Problem 7PSA

Yes, triangle VWX is an isosceles triangle.

Explanation of Solution

Given information:

RSTU is a square,

  $\overline{VR}\cong \overline{SW}$

  

Corresponding parts of congruent triangles are congruent.

  $\angle V\cong \angle W$

If corresponding angles are congruent, then their corresponding sides are also congruent.

  $\overline{XV}\cong \overline{UW}$

Triangle VWX is an isosceles triangle.

c.

To determine

To find:Triangle UTX is an isosceles triangle.

Answer to Problem 7PSA

Yes, triangle UTX is an isosceles triangle.

Explanation of Solution

Given information:

RSTU is a square,

  $\overline{VR}\cong \overline{SW}$

  

Corresponding parts of congruent triangles are congruent.

  $\angle V\cong \angle W$

If corresponding angles are congruent, then their corresponding sides are also congruent.

  $\overline{XV}\cong \overline{UW}$

By subtraction property, we get

  $\overline{XU}\cong \overline{XT}$

Triangle UTX is an isosceles triangle.