Properties of an Isosceles Trapezoid
How to solve the isosceles trapezoid problems by using its properties: definition, properties of its angles and diagonals, examples, and their solutions.
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.
Properties of a trapezoid
There are two properties
of the angles of an isosceles trapezoid.
1. The upper base angles are congruent.
And the lower base angles are congruent.
2. Two interior angles that inscribe the leg
m∠[blue] + m∠[green] = 180
This is true because
these two angles are
the consecutive interior angles in parallel lines.
Consecutive interior angles in parallel lines
∠A and ∠D are the angles
that inscribe the same leg.
m∠D = 60
So m∠A + 60 = 180.
Move +60 to the right side.
Then m∠A = 120.
∠A and ∠B are the upper base angles.
m∠A = 120
So m∠B = 120.
∠D and ∠C are the lower base angles.
m∠D = 60
So m∠C = 60.
So m∠A = 120, m∠B = 120, and m∠C = 60.
For the segments
formed by the diagonals of an iscosceles trapezoid,
the upper segments are congruent,
and the lower segments are congruent.
The given figure is an isosceles trapezoid.
So the upper segments
formed by the diagonals
So the upper right segment is 6.
the upper segment is 6
and the lower segment is 11.
So BD = 6 + 11