Look at the picture of a traditional house above.
What are you going to
To describe the properties
of a trapezoid
To define a trapezoid
To find the formula of the
area and perimeter of a
The lower roof has the form of a trapezoid. Now look at the
sides of the roof. What can you say? You may be saying that the
upper and the lower sides are parallel and others are not.
On the basis of your observation, you can define a
trapezoid as the following.
A quadrilateral with one pair of exactly parallel
Quadrilateral ABCD on the right is a
trapezoid. Side AB and DC are called the bases
of the trapezoid, sides AB and DC are
parallel, and sides AD and BC are called
the legs of the trapezoid. Quadrilateral ABCD is then called
Mathematics for Junior High School Year 7 / 333
Think and Discuss
1. Trapezoid ABCD on the left is called an
isosceles trapezoid, because the legs are
equal, AD = BC.
a. What is the relation between ∠A and ∠D;
between ∠B and ∠C? Explain.
b. What is the relation between ∠A and ∠C and between ∠B and ∠D?
c. Are ∠A = ∠D and ∠B = ∠C? Explain it.
2. Trapezoid EFGH on the left side is a right-
angled trapezoid, because one of its legs is
perpendicular to the base.
a. What are the measures of ∠E and ∠H?
b. What is the relation between ∠F and ∠G? Explain it.
Based on the result of “Think and Discuss” above, we have got the
properties of a trapezoid. They are as follows:
1. The sum of two adjacent angles between two parallel lines is
180°. (In Figure 8.10, ∠E+∠H=∠F+∠G = 180°)
2. In an isosceles trapezoid, each pair of base angles are equal.
(In Figure 8.9, ∠A = ∠B and ∠C = ∠D)
3. In an isosceles trapezoid, the diagonals are