Properties of Trapezoids
A trapezoid has exactly one pair of parallel sides, called bases. The non-parallel sides are called legs.
Introduction
Trapezoid: one pair of parallel sides (bases)
Past Knowledge
Parallel lines (3.1). Parallelogram properties (9.2). Supplementary angles.
Today's Goal
Define trapezoids, identify bases/legs, and apply the co-interior angle property.
Future Success
Isosceles trapezoids (9.3.2), kites (9.3.3), area formulas.
Key Concepts
Trapezoid Definition
- Bases (): The two parallel sides
- Legs: The two non-parallel sides
- Height (): Perpendicular distance between the bases
Key Property: Co-Interior (Same-Side) Angles
Each leg acts as a transversal between the parallel bases. So the two angles on the same leg are supplementary (sum to 180°).
Area of a Trapezoid
“Average of the bases times the height”
Worked Examples
Area
Bases are 10 and 14, height = 6. Find the area.
Area = 72 sq units
Finding a Missing Angle
Trapezoid ABCD (AB ∥ DC). ∠A = 65°. Find ∠D.
∠A and ∠D are co-interior (same leg AD):
∠D = 115°
Finding Height from Area
A trapezoid has bases 8 and 12, area = 60. Find the height.
→
h = 6
Common Pitfalls
Using the Leg as the Height
The height is the perpendicular distance between bases, not the leg length. Unless the trapezoid is a right trapezoid, the leg ≠ height.
Forgetting the ½ in the Area Formula
The trapezoid area formula has a — it's the average of the bases times the height, not the sum.
Real-Life Applications
Bridges — Truss Panels
Many bridge trusses use trapezoidal sections that distribute weight efficiently. The parallel bases provide stability while the angled legs transfer forces.
Handbag & Bag Design
Many tote bags and purses have a trapezoidal cross-section — wider at the top (opening) and narrower at the bottom for structural stability.
Practice Quiz
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