Which description does NOT guarantee that a trapezoid is isosceles?
A. congruent bases
B. congruent legs
C. both pairs of base angles congruent
D. congruent diagonals
It's C.
D. congruent diagonals
B. congruent legs
To determine which description does NOT guarantee that a trapezoid is isosceles, we need to understand the properties of an isosceles trapezoid.
An isosceles trapezoid is a trapezoid that has two parallel sides and two non-parallel sides of equal length.
Let's examine the given options:
A. Congruent bases: If the bases of a trapezoid are congruent, then it must be isosceles because having congruent bases is one of the defining properties of an isosceles trapezoid.
B. Congruent legs: If the legs of a trapezoid are congruent, then it must be isosceles because having congruent legs is also one of the defining properties of an isosceles trapezoid.
C. Both pairs of base angles congruent: If both pairs of base angles in a trapezoid are congruent, then it isnot necessarily isosceles because congruent base angles do not imply equal side lengths.
D. Congruent diagonals: If the diagonals of a trapezoid are congruent, it is not necessarily isosceles because congruent diagonals do not guarantee equal side lengths.
Therefore, the answer is option C. When both pairs of base angles are congruent in a trapezoid, it does not guarantee that the trapezoid is isosceles.