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




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.



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.




Share this page: What’s this?

Recent Articles

RSS

  1. Division of Whole Numbers |Relation between Dividend, Divisor Quotient

    Mar 05, 25 03:36 PM

    Dividing Whole Numbers
    Relation between Dividend, Divisor, Quotient and Remainder is. Dividend = Divisor × Quotient + Remainder. To understand the relation between dividend, divisor, quotient and remainder let us follow the…

    Read More

  2. Multiplication of Whole Numbers | Whole Numbers|Multiplication|Numbers

    Mar 05, 25 03:29 PM

    Multiplication of Whole Numbers
    Multiplication of whole numbers is the sort way to do repeated addition. The number by which any number is multiplied is known as the multiplicand. The result of the multiplication is known as the pro…

    Read More

  3. 12 Times Table | Read and Write Multiplication Table of 12|Times Table

    Mar 05, 25 02:29 PM

    12 times table
    In 12 times table we will learn how to read and write multiplication table of 12. We read twelve times table as: One time twelve is 12 Two times twelve are 24 Three times twelve are 36

    Read More

  4. Adding 1-Digit Number | Understand the Concept one Digit Number

    Mar 05, 25 03:08 AM

    Add by Counting Forward
    Understand the concept of adding 1-digit number with the help of objects as well as numbers.

    Read More

  5. Subtraction of Whole Numbers | Whole Number |Subtract One Large Number

    Mar 04, 25 12:20 PM

    Subtracting Whole Numbers
    Subtraction of whole numbers is discussed in the following two steps to subtract one large number from another large number: Step I: We arrange the given numbers in columns, ones under ones, tens unde…

    Read More