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:

            Statement

1. ∠SPR = ∠PRQ.

2. ∠SRP = ∠RPQ.

3. PR = PR.

4. ∆PSR ≅ ∆RQP.

5. ar(∆PSR) = ar(∆RQP). (Proved)

            Reason

1. 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).






9th Grade Math

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


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



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.



Share this page: What’s this?

Recent Articles

  1. Multiplication of a Number by a 3-Digit Number |3-Digit Multiplication

    Mar 28, 24 06:33 PM

    Multiplying by 3-Digit Number
    In multiplication of a number by a 3-digit number are explained here step by step. Consider the following examples on multiplication of a number by a 3-digit number: 1. Find the product of 36 × 137

    Read More

  2. Multiply a Number by a 2-Digit Number | Multiplying 2-Digit by 2-Digit

    Mar 27, 24 05:21 PM

    Multiply 2-Digit Numbers by a 2-Digit Numbers
    How to multiply a number by a 2-digit number? We shall revise here to multiply 2-digit and 3-digit numbers by a 2-digit number (multiplier) as well as learn another procedure for the multiplication of…

    Read More

  3. Multiplication by 1-digit Number | Multiplying 1-Digit by 4-Digit

    Mar 26, 24 04:14 PM

    Multiplication by 1-digit Number
    How to Multiply by a 1-Digit Number We will learn how to multiply any number by a one-digit number. Multiply 2154 and 4. Solution: Step I: Arrange the numbers vertically. Step II: First multiply the d…

    Read More

  4. Multiplying 3-Digit Number by 1-Digit Number | Three-Digit Multiplicat

    Mar 25, 24 05:36 PM

    Multiplying 3-Digit Number by 1-Digit Number
    Here we will learn multiplying 3-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. 1. Multiply 201 by 3 Step I: Arrange the numb…

    Read More

  5. Multiplying 2-Digit Number by 1-Digit Number | Multiply Two-Digit Numb

    Mar 25, 24 04:18 PM

    Multiplying 2-Digit Number by 1-Digit Number
    Here we will learn multiplying 2-digit number by 1-digit number. In two different ways we will learn to multiply a two-digit number by a one-digit number. Examples of multiplying 2-digit number by

    Read More