ISOSCELES TRAPEZOID WITH DIAGONALS WORKSHEET

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Find the length of the diagonal indicated for each trapezoid.

Problem 1 :

DF = 9.1, Find CE

Solution

Solve for x. Each figure is a trapezoid.

Problem 2 :

DF = 6 and CE = 2x - 10

Solution

Problem 3 :

DF = 12 and EG = -2x + 36

Solution

Find the length of the diagonal indicated for each trapezoid.

Problem 4 :

JL = 2x + 4, KM = 4x - 8. Find JL

Solution

Problem 5 :

UW = 3x + 11, TV = 8x - 9 and Find UW

Solution

Problem 6 :

The bases of an isosceles trapezoid ABCD measure 10 cm and 20 cm. The height (altitude) is 12 cm. How long are the legs AB and CD?

Solution

Problem 7 :

In isosceles trapezoid KIME, <K and <E are the base angles. If IK = 11 and ME = 3x - 1, what is the value of x?

Solution

Problem 8 :

𝐴𝐵𝐶𝐷 is an isosceles trapezoid with bases 𝐴𝐵 and 𝐷𝐶. If 𝐴𝐷 = 3x+4 and 𝐵𝐶 = x+12. Find the value of x and the length of 𝐴𝐷.

Solution

Problem 9 :

Trapezoid 𝐴𝐵𝐶𝐷 is an isosceles. Find the missing angle measures.

Solution

Problem 10 :

A hip roof slopes at the ends of the buildings as well as the front and back. The front of this hip roof is in the shape of an isosceles trapezoid. If one angle measures 30 degree, find the measures of the other three angles.

Solution

Problem 11 :

Find the length of the shorter base of a trapezoid if the length of the median is 34 meters and the length of the longer base is 49 meters.

Solution

Problem 12 :

One base angle of an isosceles trapezoid is 45 degree. Find the measures of the other three angles.

Solution

Problem 13 :

Show that the quadrilateral with vertices at Q(0, 3), R(0, 6), S(-6, 0) and T(-3, 0) is a trapezoid. Decide whether the trapezoid is isosceles. Then find the length of the midsegment of the trapezoid.

Solution

Answer Key

1) CE = 9.1

2) x = 8

3) x = 12

4) x = 6

5) x = 4

6) CD is 13.

7) x = 4

8) x = 4

∠D = 180 - 65

= 115

∠C = 115

∠A = ∠B

∠B = 65

10) the required angles are 30, 30, 150 and 150

11) the length of the shorter base is 19 meters.

12) the required angles are 45, 45, 135 and 135.

13) It is not isosceles trapezium. Since it is not isosceles trapezium, we cannot use midsegment theorem.

Problem 1 :

Trapezoid with Midsegment

x = _____, y = _____

Solution

Problem 2 :

Isosceles Trapezoid with Midsegment

x = _____, y = _____

Solution

Problem 3 :

Trapezoid with Midsegment

x = _____, y = _____

Solution

Problem 4 :

Trapezoid with Midsegment

x = _____, Perimeter = _____

Solution

Problem 5 :

Isosceles Trapezoid with Midsegment

x = _____, y = _____

Solution

Problem 6 :

Isosceles Trapezoid with Midsegment

x = _____, y = _____

Solution

Problem 7 :

In the diagram MN is the midsegment of trapezoid PQRS. Find MN.

Solution

Problem 8 :

Find the length of midsegment YZ in trapezoid STUV.

Solution

Problem 9 :

Find the value of x

Solution

Problem 10 :

Find the value of x

Solution

Answer Key

1) the values of x and y is 4 and 20.

2) the values of x and y is 2 and 23.

3) the values of x and y is 13 and 23.

4) the value of x is 5 and Perimeter = 14 units.

5) the values of x and y is 13.75 and 22.

6) the values of x and y is 5 and 5.

7) the length of MN is 20 inches.

8) the length of ZY is 3√5 units.

9) the value of x is 3.

10) the value of x is 6.

Find x.

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Problem 9 :

Problem 10 :

You can use a trapezoid to approximate the shape of Scott County, Virginia. The population is about 23,200. About how many people are there per square mile?