Chapter 6.1, Problem 14PSB

To determine

To show that sides TR and VS are congruent.

Answer to Problem 14PSB

Sides $\overline{TR}and\overline{VS}arecongruent.$

Explanation of Solution

Given information:

Planes m and n intersect in $\overleftrightarrow{RS}$ .

Plane m contains R, S, and V.

Plane n contains R, S, and T.

  $\begin{array}{l}\overline{TS}\cong \overline{VR}\\ \overline{TR}\perp \overline{RS}\\ \overline{VS}\perp \overline{RS} \end{array}$

Formula used:

The below properties are used:

Perpendicular lines form right angles.

Two triangles are congruent by HL congruence rule.

Proof:

It is given that,

Planes m and n intersect in $\overleftrightarrow{RS}$ .

Plane m contains R, S, and V.

Plane n contains R, S, and T.

  $\begin{array}{l}\overline{TS}\cong \overline{VR}\\ \overline{TR}\perp \overline{RS}\\ \overline{VS}\perp \overline{RS} \end{array}$

  

Perpendicular lines form right angles.

  $\angle TRSand \angle VSRarerightangles.$

By reflexive property, we get

  $\overline{RS} \cong \overline{RS}$

By HL congruence rule, we get

  $\Delta TRS \cong \Delta VSR$

As corresponding parts of congruent triangles are congruent, we get

  $\overline{TR} \cong \overline{VS}$