Properties of trapezoids

Learning Objectives Identify a trapezoid and its key parts (bases, legs, base angles, median). State and apply the property that consecutive angles between parallel bases are supplementary. Define an isosceles trapezoid and prove its key properties, including congruent base angles and congruent diagonals. State and apply the Trapezoid Median Theorem to find unknown lengths. Solve for unknown angles and side lengths in trapezoids using algebraic expressions. Construct simple geometric proofs involving trapezoids. Ever noticed the shape of a bridge's support structure or a classic handbag? 👜 You're likely looking at a trapezoid! In this tutorial, we will explore the trapezoid, a unique member of the quadrilateral family. We will define its parts, uncover the specia...

TermDefinitionExample TrapezoidA quadrilateral with exactly one pair of parallel sides.In quadrilateral ABCD, if side AB is parallel to side DC, but side AD is not parallel to side BC, then ABCD is a trapezoid. Bases and LegsThe parallel sides of a trapezoid are called the bases. The non-parallel sides are called the legs.In trapezoid ABCD with AB || DC, AB and DC are the bases, while AD and BC are the legs. Base AnglesA pair of angles that share a common base. Every trapezoid has two pairs of base angles.In trapezoid ABCD with base DC, ∠D and ∠C form one pair of base angles. ∠A and ∠B form the other pair. Isosceles TrapezoidA trapezoid in which the legs (non-parallel sides) are congruent.If trapezoid ABCD has AB || DC and the length of leg AD is equal to the length of leg BC, it is an is...

Consecutive Angles Property In a trapezoid, consecutive angles between the two parallel bases are supplementary. If base₁ || base₂, then m∠A + m∠D = 180° and m∠B + m∠C = 180°. Use this rule to find the measure of an unknown angle when you know the measure of the other angle sharing the same leg. This is a direct application of the Consecutive Interior Angles Theorem for parallel lines. Isosceles Trapezoid Theorems 1. Base angles are congruent (e.g., ∠D ≅ ∠C and ∠A ≅ ∠B). 2. Diagonals are congruent (AC ≅ BD). These properties apply ONLY to isosceles trapezoids. If you know a trapezoid is isosceles, you can assume these are true. Conversely, if a trapezoid has congruent base angles or congruent diagonals, you can prove it is isosceles. Trapezoid Median Theorem The length...