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

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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.

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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.

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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.