## Friday, July 26, 2013

### Proving - Congruent Triangles, 2

Category: Plane Geometry

"Published in Newark, California, USA"

In the given figure, if MR PN; NR MP, prove that ∆NOR
∆MOP.

 Photo by Math Principles in Everyday Life

Solution:

Consider the given figure above

 Photo by Math Principles in Everyday Life

Proof:

1. Statement: MR PN and NR MP.

Reason: Given items.

2. Statement: PR PR

Reason: Reflexive property of congruence.

3. Statement: ∆MRP ∆NPR

Reason: Side Side Side (SSS) Postulate.

4. Statement: ∠MPR ≅ NRP
∠PMR ≅ ∠PNR
∠PRM ≅ RPN

Reason: Since ∆MRP ≅ NPR, then all interior angles of a triangle are congruent to all interior angles of other triangle.

5. Statement: ∠PRM ≅ 4 and ∠RPN ≅ 3.

Reason: Reflexive property of congruence.

6. Statement: ∠PRM ≅ RPN ≅ 3 ≅ 4

Reason: Transitive property of congruence.

7. Statement: ∆POR is an isosceles triangle.

Reason: The two angles of an isosceles triangle are congruent. Hence, 3 ≅ 4 at the base.

8. Statement: OP OR

Reason: Since ∆POR is an isosceles triangle, then the two sides of an isosceles triangle are congruent.

9. Statement: MPR = 1 + 3 and NRP = 2 + ∠4