10
The trapezoid
Textbook: pp. 29–31
GoalKnow the definition, parts and kinds of a trapezoid and find its angles.
New words
trapezoid · trapetsiyabases · asoslarlegs · yon tomonlaraltitude of a trapezoid · trapetsiya balandligi
Explanation
A quadrilateral with two parallel sides and two sides that are not parallel is called a trapezoid. The parallel sides are its bases and the other two are its legs. The distance between the lines of the bases is the altitude of the trapezoid. A trapezoid with equal legs is isosceles, and one with a right angle is a right trapezoid. The two angles at one leg add up to 180°, because they are interior angles on the same side. A right trapezoid has two right angles.
Worked examples
In trapezoid ABCD, BC ∥ AD and ∠A = 65°. A and B are interior angles on the same side, so ∠B = 180° − 65° = 115°.
In a right trapezoid ∠A = 90° and ∠D = 58°. Then ∠B = 90° and ∠C = 180° − 58° = 122°.
Class activity
“Find the trapezoid”: spot trapezoid shapes among classroom objects and point out their bases and legs.
Practice
1
In trapezoid ABCD, BC ∥ AD and ∠A = 72°. How many degrees is ∠B?
108
2
In the same trapezoid ∠D = 54°. How many degrees is ∠C?
126
3
In a right trapezoid the other angle at the larger base is 62°. How many degrees is the angle at the smaller base next to the same leg?
118
4
Why can a trapezoid not have two pairs of parallel sides?
By definition its legs are not parallel; with two pairs of parallel sides it would be a parallelogram.