Chapter 7.2, Problem 19PSC

Solution

To Prove: The congruency of $\Delta NPR$ with respect to $\Delta SPR$

Given information: P, T and R lie in plane f, $\angle TNR\cong \angle TSR$ , $\overline{NS}\perp f$ and $\angle TNP\cong \angle TSP$ provided in the question which will help to find the solution.

Proof: Here, $\angle TNR\cong \angle TSR$ (given)

Hence, SR=RN (sides opposite to congruent angles are equal)

And, $\angle TNP\cong \angle TSP$ (given)

So that, SP=PN (sides opposite to congruent angles are equal)

So that, In $\Delta NPR$ and $\Delta SPR$

SP=PN (proved above)

SR=RN (proved above)

PR=PR (common)

Hence, $\Delta NPR\cong \Delta SPR$ (by using Side Side Side property)