Chapter 6.2, Problem 7PSB

To determine

To prove: The angle PQS is right angle

Explanation of Solution

Given information:

Given points Q, R, S, and T lie in the given plane m

Given two angles PQR and PQT are right angles

Formula used:

Congruency means same shape and same size

Congruent Parts of congruent Triangles are Congruent

Reflexive property

If a line is perpendicular to plane than all line passing through its foot will also perpendicular to it

Perpendicular lines always form right angles

Proof:

Points Q, R, S and T lie in the plane m...........given

  $\overline{\text{PQ}}\perp \overline{\text{QS}},\overline{\text{PQ}}\perp \overline{\text{RQ}}\text{ \& }\overline{\text{PQ}}\perp \overline{\text{QT}}$........... If a line is perpendicular to plane than all line passing through its foot will also perpendicular to it

  $\angle \text{PQR}=\angle \text{PQT}=90°$ ........... given

  $\overline{\text{PR}}\cong \overline{\text{PS}}$ , $\overline{\text{PT}}\cong \overline{\text{PS}}$ & $\overline{\text{PT}}\cong \overline{\text{PR}}$ ........... reflexive property

  $\therefore \Delta \text{PQR}\cong \Delta \text{PQS}$ and $\Delta \text{PQR}\cong \Delta \text{PQT}$

  $\angle PQS=90°$ ........... congruent Parts of congruent Triangles are congruent