How to Understand the Key Properties of Trapezoids

• Isosceles Trapezoid: A trapezoid in which the non-parallel sides (legs) are congruent. In this type of trapezoid, base angles are congruent.
• Non-Isosceles Trapezoid: Base angles are not necessarily congruent.

Examples

Practice Questions:

1. If one pair of opposite sides in a quadrilateral is parallel and the other pair is non-parallel, what type of quadrilateral is it?
2. In a trapezoid, if the non-parallel sides are of equal length, what special name is given to this trapezoid?
3. True or False: The diagonals of an isosceles trapezoid are always equal in length.
4. In a trapezoid \(ABCD\) where \(AB\) is parallel to \(CD\), if angle \(A\) measures \(75^\circ\), what would be the measure of angle \(C\) given that the angles on the same side of the non-parallel line are supplementary?

1. Trapezoid.
2. Isosceles trapezoid.
3. True.
4. \(105^\circ\) (since \(180^\circ – 75^\circ = 105^\circ\)).

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