Study Guides/Maths/Are Diagonals of a Parallelogram Equal?
Study Guide · Maths

Are the Diagonals of a Parallelogram Equal?

One of the most frequently asked questions in Class 8 and 9 Geometry is whether the diagonals of a parallelogram are equal in length.

The short answer is: No, the diagonals of a general parallelogram are NOT equal.

Question (Click to Flip)

Do the diagonals of a parallelogram divide it into equal triangles?

Answer

Yes! A single diagonal divides a parallelogram into two congruent triangles. If you draw both diagonals, they divide the parallelogram into four triangles of equal area (though they are not all congruent to each other).

Card 1 of 1 free previews

Key Facts

If you are given a parallelogram and told that its diagonals are equal, you have just proved that the parallelogram is actually a rectangle. This is a standard theorem proof in Class 9 Maths.

Diagonals of a Standard Parallelogram

In a standard parallelogram (where all angles are not 90° and all sides are not equal):

  1. They are NOT equal: One diagonal is longer than the other.
  2. They DO bisect each other: They cut each other exactly in half. If the diagonals are AC and BD intersecting at O, then AO = OC and BO = OD.
  3. They are NOT perpendicular: They do not cross at 90° angles.

When ARE the Diagonals Equal?

The diagonals of a parallelogram are equal ONLY if the parallelogram is a Rectangle or a Square.

Because rectangles and squares have 90° angles, the distance between the opposite corners becomes exactly the same.

  • Rectangle: Diagonals are Equal & Bisect each other.
  • Square: Diagonals are Equal, Bisect each other, AND are Perpendicular (90°).

What about a Rhombus?

A rhombus is a special parallelogram where all 4 sides are equal.

  • Are its diagonals equal? No.
  • Do they bisect each other? Yes.
  • Are they perpendicular? Yes (They cross exactly at 90°).

So, a rhombus has perpendicular diagonals, but they are not equal in length (unless the rhombus is a square).

Summary Table of Quadrilateral Diagonals

QuadrilateralAre Diagonals Equal?Do they Bisect?Are they Perpendicular?
Parallelogram❌ No✅ Yes❌ No
Rectangle✅ Yes✅ Yes❌ No
Rhombus❌ No✅ Yes✅ Yes
Square✅ Yes✅ Yes✅ Yes

Questions and Answers

Do the diagonals of a parallelogram divide it into equal triangles?+

Yes! A single diagonal divides a parallelogram into **two congruent triangles**. If you draw both diagonals, they divide the parallelogram into **four triangles of equal area** (though they are not all congruent to each other).

More in Maths

📐

Formula for Number of Diagonals in a Polygon

Learn the formula for the number of diagonals in any polygon. Solve for triangle, quadrilateral, pentagon, hexagon with step-by-step examples.

📐

Number Series Questions — Patterns and Types

Learn how to solve number series questions for school maths and competitive exams. Covers arithmetic, geometric, Fibonacci, and mixed series.

📐

Number System — Lakh, Crore, Million Conversions

Learn key number conversions: 0.1 lakh, 1 crore zeros, 10 crore, 10 million to lakh, 100000 spelling. Complete Indian and international number system guide.

📐

One Cent is Equal to How Many Square Feet?

How many square feet are there in one cent of land? Learn the exact conversion rate used in South Indian real estate (1 Cent = 435.6 sq ft).

📐

One Crore in Numbers

Learn how one crore is written in numbers. Understand the Indian number system and convert crore to million, billion with examples.

Study Smarter with Shinyu.ai

Turn this guide into revision flashcards, a practice exam, or an AI-generated podcast — free, no signup required.