Iso-trap base ∠ — Isoceles trapezoid: base angles equal · Principia

Dependencies: Parallelogram tests, Parallelogram properties (opposite sides equal, diagonals bisect each other), Base angles of an isoceles triangle are equal, Parallel ⇒ corresponding angles equal (converse).

Statement

Let $ABCD$ be an isosceles trapezoid:

AD \parallel BC,\qquad |AB| = |CD|,

where $AD$ is the upper base (shorter), $BC$ is the lower base (longer), and $AB$ , $CD$ are the two legs. Then the two base angles on the same base are equal:

\angle ABC \;=\; \angle DCB.

$Isosceles trapezoid ABCD (AD \parallel BC, legs AB = CD): the two base angles on the same base satisfy \angle ABC = \angle DCB.$

Isoceles trapezoid: base angles equal

Statement

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