PROPERTIES OF ISOSCELES TRAPEZOID WORKSHEET

Each trapezoid is isosceles. Find the measure of each angle.

Problem 1 :

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Problem 2 :

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Problem 3 :

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Problem 4 :

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Problem 5 :

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Problem 6 :

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Problem 7 :

In trapezoid LMNO below, median PQ is drawn.

If LM = x + 7, ON = 3x + 11, and PQ = 25, what is the value of x?

a) 1.75    b) 3.5      c) 8     d) 17

Solution

Problem 8 :

In the diagram below, LATE is an isosceles trapezoid with LE ≅ AT, LA = 24, ET = 40, and AT =10. Altitudes LF and AG are drawn

What is the length of LF?

a) 6      b) 8     c) 3      d) 4

Solution

Problem 9 :

In the diagram below of isosceles trapezoid ABCD, AB = CD = 25, AD = 26, and BC = 12.

What is the length of an altitude of the trapezoid?

a) 7      b) 14     c) 19      d) 24

Solution

Problem 10 :

In isosceles trapezoid ABCD, AB ≅ CD. If BC = 20, AD = 36, and AB = 17, what is the length of the altitude of the trapezoid?

a) 10      b) 12     c) 15     d) 16

Solution

Problem 11 :

In trapezoid ABCD below, AB || CD

If AE = 5.2, AC = 11.7, and CD = 10.5, what is the length of AB, to the nearest tenth?

a) 4.7     b) 6.5     c) 8.4      d) 13.1

Solution

Problem 12 :

The diagram below shows isosceles trapezoid ABCD with AB || DC and AD ≅ BC. If m∠BAD = 2x and m∠BCD = 3x + 5, find m∠BAD.

Solution

Find the value of the variable in each isosceles trapezoid.

Problem 1 :

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Problem 2 :

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Problem 3 :

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Problem 4 :

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Problem 5 :

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Problem 6 :

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Problem 7 :

If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral could be a

a) rectangle     b) rhombus      c) square      d) trapezoid

Solution

Problem 8 :

In trapezoid RSTV with bases RS and VT, diagonals RT and SV intersect at Q

If trapezoid RSTV is not isosceles, which triangle is equal in area to RSV?

a) RQV        b) RST       c) RVT         d) SVT

Solution

Problem 9 :

In the diagram below of isosceles trapezoid STAR, diagonals AS and RT intersect at O and ST || RA, with nonparallel sides SR and TA.

Which pair of triangles are not always similar?

a) STO and ARO         b) SOR and TOA

c) SRA and ATS          d) SRT and TAS

Solution

Problem 10 :

Isosceles trapezoid ABCD has diagonals AC and BD. If AC = 5x + 13 and BD = 11x − 5, what is the value of x?

a) 28      b) 10  3/4      c) 3      d) 1/2

Solution

Problem 11 :

The cross section of an attic is in the shape of an isosceles trapezoid, as shown in the accompanying figure. If the height of the attic is 9 feet, BC = 12 feet, and AD = 28 feet, find the length of AB to the nearest foot.

Solution

Problem 1 :

In the figure, YZ is the midsegment of trapezoid TWRV.  Determine the value of x.

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Problem 2 :

Solve for x.

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Problem 3 :

Find the length of TU.

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Problem 4 :

CD is the midsegment of trapezoid WXYZ.

a. What is the value of x?

b. What is XY?

c. What is WZ?

Solution

Problem 5 :

Find the length of the midsegment of the trapezoid with the given vertices.

S(0, 0) T(2, 7) U(6, 10) and V(8, 6)

Solution

Problem 6 :

In the diagram, NP = 8 inches, and LR = 20 inches. What is the diameter of the bottom layer of the cake?

Solution

Problem 7 :

The bases of a trapezoid lie on the lines y = 2x + 7 and y = 2x − 5. Write the equation of the line that contains the midsegment of the trapezoid.

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Problem 8 :

In the figure above, EO is the midsegment of trapezoid TRAP and RP intersect EO at point Z. If RA = 15 and EO = 18, what is the length of TP?

Solution

Problem 9 :

You are building a plant stand with three equally-spaced circular shelves. The diagram shows a vertical cross section of the plant stand. What is the diameter of the middle shelf?

Solution

Problem 10 :

Find the length of the midsegment EF in trapezoid ABCD and verify the distance between EF using distance between two points formula.

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