WORKSHEET ON TRAPEZOIDS

Problem 1 :

Trapezoid PQRS given below is an isosceles trapezoid.

Find m∠P, m∠Q and m∠R.

Problem 2 :

Prove that the figure ABCD given below is a trapezoid.

Problem 3 :

A baker is making a cake like the one which is given below. The top layer of the cake has a diameter of 8 inches and the bottom layer has a diameter of 20 inches. How big should the middle layer of the cake be?

1. Answer :

Given : PQRS is an isosceles trapezoid.

According to theorem 1 above, each pair of base angles in an isosceles trapezoid must be congruent.

So, we have

m∠S = m∠R = 50°

Because ∠S and ∠P are consecutive interior angles formed by parallel lines, they are supplementary.

So, we have

m∠S + m∠P = 180°

Substitute m∠S = 50°.

50° + m∠P = 180°

Subtract 50° from both sides.

m∠P = 130°

According to theorem 1 above, each pair of base angles in an isosceles trapezoid must be congruent.

So, we have

m∠P = ∠Q = 130°

Hence,

m∠P = 130°

m∠Q = 130°

m∠R = 50°

2. Answer :

Find the slope of each side of the figure ABCD above and compare the slopes of opposite sides.

We can find the slope using slope formula given below.

Slope of the line joining two points (x₁, y₁) and (x₂, y₂) :

Slope of AB = (5 - 0)/(0 - 5) = 5/(-5) = -1

Slope of CD = (4 - 7)/(7 - 4) = -3/3 = -1

Because the slopes of AB and CD are equal, we have

AB || CD

Slope of BC = (7 - 5)/(4 - 0) = 2/4 = 1/2

Slope of AD = (4 - 0)/(7 - 5) = 4/2 = 2

The slopes of BC and AD are not equal. So BC and AD are not parallel.

Because AB ∥ CD and BC ∦ AD, ABCD is a trapezoid.

3. Answer :

In the diagram given above, EFCH is an isosceles trapezoid and DG is the midsegment of the trapezoid.

And also, DG is the diameter of middle layer of the cake.

Using the Midsegment Theorem for Trapezoids, we have

DG = 1/2 ⋅ (EF + CH)

= 1/2 ⋅ (8 + 20)

= 1/2 ⋅ (28)

= 14

Hence, the diameter of the middle layer of the cake is 14 inches.

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