# Every Diagonal of a Parallelogram Divides it into Two Triangles of Equal Area

Here we will prove that every diagonal of a parallelogram divides it into two triangles of equal area.

Given: PQRS is a parallelogram in which PQ SR and SP RQ. PR is a diagonal of the parallelogram.

To prove: ar(∆PSR) = ar(∆RQP).

Proof:

 Statement1. ∠SPR = ∠PRQ.2. ∠SRP = ∠RPQ.3. PR = PR.4. ∆PSR ≅ ∆RQP. 5. ar(∆PSR) = ar(∆RQP). (Proved) Reason1. SP ∥ RQ and PR is a transversal.2. PQ ∥ SR and PR is a transversal.3. Common side.4. By ASA axiom of congruency. 5. By area axiom for congruent figures.

Note: ar(∆PSR) = ar(∆PQR) = $$\frac{1}{2}$$ × ar(parallelogram PQRS).

From Every Diagonal of a Parallelogram Divides it into Two Triangles of Equal Area to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles 1. ### Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

Dec 01, 23 01:16 AM

There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

2. ### Days of the Week | 7 Days of the Week | What are the Seven Days?

Nov 30, 23 10:59 PM

We know that, seven days of a week are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday. A day has 24 hours. There are 52 weeks in a year. Fill in the missing dates and answer the questi…