Isosceles Trapezoid

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Isosceles trapezoid is a trapezoid has its two non parallel sides of equal length. In addition to it, the base angle that the left non parallel side makes with the base is equal to the base angle that the right non parallel side makes with the base.

In the isosceles trapezoid shown above lengths of non parallel side AD and BC are equal to c. Also the base angle A is equal to base angle B.

Example 1: Given a trapezoid PQRS with the measure of the sides as given below:

PQ = 5 cm, QR = 3 cm, RS = 2 cm, SP = 3 cm

Sides PQ and RS are parallel sides. Is the given trapezoid an isosceles trapezoid? Give reasons for your answer.

Solution: Since the sides PQ and RS are parallel sides of the trapezoid. So the two non – parallel sides are QR and SP.

The length of the two non – parallel sides is given to be equal to 3 cm. This shows that the given trapezoid is an

isosceles trapezoid.

Example 2: The angle measures of the trapezoid DEFG are given below:

angle D = 62 degree, angle E = 68 degree, angle F = 110 degree, angle G = 120 degree If angles D and E are the

angles between the lower base and the two non – parallel sides, is the trapezoid isosceles or not?

Solution: Since the two base angles D and E are not equal in measure, hence the given trapezoid DEFG is not isosceles

trapezoid.