Question

3.
Given: PT LTR, MR I TR, PT = MR
Prove: APTR = AMRT
P
T
R
M

Answer 1

To prove that ΔPTR = ΔMRT, we need to show that their corresponding sides and angles are congruent.

Step-by-step explanation:

To prove that ΔPTR = ΔMRT, we need to show that their corresponding sides and angles are congruent.

Given:

PT ⊥ TR (Perpendicular)

MR ⊥ TR (Perpendicular)

PT ≅ MR (Congruent)

To prove:

ΔPTR = ΔMRT

Proof:

1. PT ⊥ TR (Given)

2. MR ⊥ TR (Given)

3. PT ≅ MR (Given)

4. ∠PTR = ∠MRT (Right angles are congruent)

5. ∠TPR = ∠MRT (Vertical angles are congruent)

6. Triangles PTR and MRT have two pairs of congruent angles and a congruent side (PT ≅ MR).

7. By the Angle-Angle-Side (AAS) criterion, ΔPTR ≅ ΔMRT.

Therefore, ΔPTR = ΔMRT by AAS. QED.