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.

In which parallelogram the lengths of the diagonals are equal?

rectangle
A parallelogram with one right angle is a rectangle. A quadrilateral whose diagonals are equal and bisect each other is a rectangle.

Can the diagonals in a parallelogram be the same length?

Theorem 5: A rectangle is a parallelogram. Theorem 6: A rectangle is a parallelogram if and only if the diagonals are the same length. Definition 3: A rhombus is a quadrilateral where all four sides have the same length. Theorem 7: A rhombus is a parallelogram.

Is a parallelogram always a rectangle yes or no?

Parallelograms are quadrilaterals with two sets of parallel sides. Since squares must be quadrilaterals with two sets of parallel sides, then all squares are parallelograms. A parallelogram is a rectangle. This is sometimes true.

How do you prove that in a parallelogram the diagonals are equal?

Now let us start with considering a Parallelogram ABCD with diagonals AC and BD equal. Now since ABCD is a parallelogram we know opposite sides are equal. We have now triangle ADC and triangle BCD, AD = BC, AB = CD and AC = BD. Now since the two triangles are Congruent corresponding angles are also congruent.

How do you find the lengths of the diagonals of a parallelogram?

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 ⁡

When must a parallelogram be a rectangle?

Remember, for a parallelogram to be a rectangle is must have four right angles, opposite sides congruent, opposite sides parallel, opposite angles congruent, diagonals bisect each other, and diagonals are congruent.

How do you prove that the diagonals of a parallelogram bisect each other?

Expert Answer:

1. ABCD is a parallelogram, diagonals AC and BD intersect at O.
2. In triangles AOD and COB,
3. DAO = BCO (alternate interior angles)
4. AD = CB.
5. ADO = CBO (alternate interior angles)
6. AOD COB (ASA)
7. Hence, AO = CO and OD = OB (c.p.c.t)
8. Thus, the diagonals of a parallelogram bisect each other.