Isosceles Trapezoid: Property
How to use the properties of an isosceles trapezoid to solve the related problems: definition, 2 properties (angles, diagonals), 2 examples, and their solutions.
Definition
An isosceles trapezoid is a trapezoid
whose legs are congruent.
Just like an isosceles triangle,
its base angles are also congruent.
An isosceles trapezoid is also a trapezoid.
So an isosceles trapezoid
has all the properties of a trapezoid.
PropertyInterior Angles
For an isosceles trapezoid,
two interior angles
that inscribe the same base
are congruent.
m∠1 = m∠1'
m∠2 = m∠2'
And two interior angles
that inscribe the same leg
are supplementary.
m∠1 + m∠2 = 180
m∠1' + m∠2' = 180
(This is also true for a trapezoid.)
Example
The given quadrilateral is an isosceles trapezoid.
∠A and ∠D are the interior angles
that inscribe the same left leg.
m∠D = 60
So m∠A + [60] = 180.
Move +60 to the right side.
Then m∠A = 120.
Write 120º on ∠A.
∠A and ∠B are the interior angles
that inscribe the same top base.
∠A is 120º.
So ∠B is 120º.
∠D and ∠C are the interior angles
that inscribe the same bottom base.
∠D is 60º.
So ∠C is 60º.
Write m∠A, m∠B, and m∠C.
So
m∠A = 120
m∠B = 120
m∠C = 60
is the answer.
PropertyDiagonals
For an isosceles trapezoid,
four segments are formed by the diagonals.
The top two segments are congruent (blue).
And the bottom two segments are congruent. (brown)
Example
The given quadrilateral is an isosceles trapezoid.
By the diagonals AC and BD,
four segments are formed.
The top two segments are congruent:
AP = BP = 6.
The bottom two segments are congruent:
PD = PC = 11.
See BD.
BP = 6
PD = 11
So BD = 6 + 11.
6 + 11 = 17
So BD = 17.