# Is the diagonals of a parallelogram are equal in length show that the parallelogram is a rectangle?

Table of Contents

- 1 Is the diagonals of a parallelogram are equal in length show that the parallelogram is a rectangle?
- 2 What is the length of the diagonal of a parallelogram equal?
- 3 Is the diagonal of parallelogram is same?
- 4 How do you find the diagonal of a parallelogram?
- 5 How do you figure out if a parallelogram is a rectangle?
- 6 What does each diagonal do to a parallelogram?
- 7 Does a rectangle have equal diagonals in a rhombus?
- 8 Is PQRS a rectangle or a rectangle?

## Is the diagonals of a parallelogram are equal in length show that the parallelogram is a rectangle?

Solution: Given: The diagonals of a parallelogram are equal. Hence, ∠B = ∠D = ∠C = ∠A = 90° [Since opposite angles of a parallelogram are equal]. Since ABCD is a parallelogram and one of its interior angles is 90°, ABCD is a rectangle.

## What is the length of the diagonal of a parallelogram equal?

Originally Answered: Are the diagonals of a parallelogram equal? No, unless the parallelogram happens to be a rectangle. Draw pictures. Actually you can calculate the lengths of the two diagonals of a parallelogram: assume the two adjacent sides of the parallelogram have lengths a and b, with angle θ b/w them.

**Is the length of the diagonals of a parallelogram are equal then which of this condition is always true?**

If the diagonals of a parallelogram are equal in length, then prove that the parallelogram is a rectangle.

**Is a parallelogram a rectangle if the diagonals are congruent?**

If a parallelogram is a rectangle, then its diagonals are congruent. If one angle of a parallelogram is a right angle, then the parallelogram is a rectangle. If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. If a quadrilateral is a rhombus, then it is a parallelogram.

### Is the diagonal of parallelogram is same?

The opposite angles of a parallelogram are equal. The consecutive angle of a parallelogram is supplementary. If one angle is a right angle, all the angles are right angles in a parallelogram. The diagonals of a parallelogram bisect each other.

### How do you find the diagonal of a parallelogram?

FAQs on Diagonal of Parallelogram Formula For any parallelogram abcd, the formula for the lengths of the diagonals are, p=√x2+y2−2xycosA=√x2+y2+2xycosB p = x 2 + y 2 − 2 x y cos A = x 2 + y 2 + 2 x y cos B and q=√x2+y2+2xycosA=√x2+y2−2xycosB q = x 2 + y 2 + 2 x y cos A = x 2 + y 2 − 2 x y cos

**How do you find the length of the longer diagonal of a parallelogram?**

Explanation: In a parallelogram, the diagonals bisect each other, so you can set the labeled segments equal to one another and then solve for . \displaystyle 20 – 3x = 2x – 4 \rightarrow 24 = 5x \rightarrow 4.8 = x. Then, substitute 4.8 for in each labeled segment to get a total of 11.2 for the diagonal length.

**Does a parallelogram have opposite sides that are equal?**

Definition 1: A parallelogram is a four sided figure where the opposite sides are parallel. Theorem 1: In a parallelogram, the opposite sides are of equal length. Theorem 2: If the opposite sides in a quadrilateral are the same length, then the figure is a parallelogram.

#### How do you figure out if a parallelogram is a rectangle?

If a parallelogram is known to have one right angle, then repeated use of co-interior angles proves that all its angles are right angles. If one angle of a parallelogram is a right angle, then it is a rectangle.

#### What does each diagonal do to a parallelogram?

The diagonals of a parallelogram bisect each other. In any parallelogram, the diagonals (lines linking opposite corners) bisect each other. That is, each diagonal cuts the other into two equal parts.

**How do you prove that a parallelogram is a rectangle?**

Again the two coenterior angles of parallelogram being equal makes each to be 180°/2=90°.Any angle of a parallelogram being 90° proves the existence of rectangle. If the diagonals of a parallelogram are equal in length, then the parallelogram is either: A rectangle, if all the sides are not equal in length.

**Are the diagonals of a parallelogram of equallumerable angles?**

When a parallelogramis divided into two triangles we get to see that the angles across the common side( here the diagonal) are equal. This proves that the opposite angles in a parallelogramare also equal. The diagonalsof a parallelogramare not of equallength.

## Does a rectangle have equal diagonals in a rhombus?

A rectangle is not a rhombus in general, nor does a rhombus have equal diagonals — you can easily draw one that doesn’t — unless itis a square. , Ph.D. in Civil Engineering.

## Is PQRS a rectangle or a rectangle?

Since PQRS is a parallelogram and one of its interior angles is 90º, PQRS is a rectangle. 8 clever moves when you have $1,000 in the bank. We’ve put together a list of 8 money apps to get you on the path towards a bright financial future. Given that the diagonals AC and BD of parallelogram ABCD are equal in length . Consider triangles ABD and ACD.