Trapezoid: Property
How to use the properties of a trapezoid to solve the related problems: definition, 2 properties (angles, median), 2 examples, and their solutions.
Definition
A trapezoid is a quadrilateral
that have a pair of parallel sides.
Base: Parallel sides
Legs: Non-parallel sides
PropertyInterior Angles
For a trapezoid,
two interior angles that inscribe the same leg
are supplementary.
m∠1 + m∠2 = 180
m∠1' + m∠2' = 180
Example
The given quadrilateral is a trapezoid.
These two angles inscribe the same left leg.
So [x + 40] + [60] = 180.
+40 + 60 = +100
Move +100 to the right side.
Then x = 80.
Next, these two angles inscribe the same right leg.
So [8y] + [108] = 180.
Move +108 to the right side.
Then 8y = 72.
Divide both sides by 8.
Then y = 9.
x = 80
y = 9
Write these below.
So
x = 80
y = 9
is the answer.
PropertyMedian
The median of a trapezoid
is a line segment
that connects the midpoints of the legs.
It's like the midsegment of a triangle.
The median has two properties.
The median and the bases are parallel.
The median (m) and the bases (b1, b2)
satisfy this formula:
m = [1/2](b1 + b2).
Example
The given quadrilateral is a trapezoid.
The blue segment connects
the midpoints of two legs.
So the blue segment is the median.
The median is x.
The bases are 3 and 7.
So x = [1/2](3 + 7).
(3 + 7) = 10
10/2 = 5
So x = 5.