Last modified on June 11th, 2022

chapter outline

 

Diagonals of a Trapezoid

The diagonals of a trapezoid are the straight line segments linking its opposite vertices or corners.

Diagonals of a Trapezoid

Are the diagonals of any trapezoid are congruent?

NO. The diagonals of any trapezoid is not congruent. Let us learn when the diagonals of a trapezoid are congruent.

Diagonals of an Isosceles Trapezoid

The diagonals of an isosceles trapezoid are congruent. This is a special case of a trapezoid when its 2 legs are equal in length. So the diagonals are also congruent.

Diagonals of an Isosceles Trapezoid

Do the diagonals of a trapezoid bisect each other?

NO. The diagonals a trapezoid do not bisect each other.

Let us solve an example to understand the concept better.

Find the length of the diagonal of an isosceles trapezoid given.

Solution:

As we know,
Long base (a) = 18 cm, short base (b) = 12 cm
Now,
We draw in a perpendicular to BC at P.
Now,
a – b
= 18 – 12
= 6 cm
∴ PC = 6/2 = 3 cm
Applying Pythagorean’s Theorem,
In ΔDPC,  DP2 + PC2 = DC2
DP2 = √(DC2 – PC2)
= √(9.52 – 32)
= 9.01 cm
Now in ΔBPD,  BD2 = BP2 + DP2
BP = BC – PC
= 18 – 3
= 15 cm
BD = √(BP2 + DP2)
= √(152 + 9.012)
= √(225 + 81.2)
≈ 17.50 cm

Last modified on June 11th, 2022

Leave a Reply

Your email address will not be published.