FIND MISSING LENGTH AND ANGLES IN ISOSCELES TRAPEZIUM WORKSHEET

Find the value of the variable in each isosceles trapezoid.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

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

Find the measurement of the angle indicated for each trapezoid.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Given isosceles trapezoid 𝐴𝐵𝐶𝐷, 𝐵𝐶 ∥ 𝐴𝐷. If 𝑚 < 𝐴 = 3(2x − 7) and 𝑚 < 𝐶 = 4x + 1, find the value of x. Find the measure of all of the angles.

Solution

Problem 7 :

Find ∠V

Solution

Problem 8 :

Find ∠M

Solution

Problem 9 :

Isosceles trapezoid ABCD with BC ||AD. If m∠A = 4x+20 and m∠D = 2x+38, find m∠A, m∠B, m∠C, and m∠D.

Solution

Problem 10 :

In isosceles trapezoid ABCD, BC||AD. The measure of ∠ADC = 4x+20 and the measure of ∠DAB = 8x - 20. Find the value of x, ∠ADC, ∠DAB, ∠BCD, and ∠ABC.

Solution

Problem 11 :

Solve for x. Find m∠R

Solution

Problem 12 :

Solve for x. Find m∠V

Solution

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

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

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

Answer Key

1) 

∠1 = 77^º

∠2 = 103^º

∠3 = 103^º

2)

∠1 = ∠2 = 69

∠3 = 111

3) 

∠2 = 131

∠3 = 131

4)

∠W = 75

∠Z = 75

5)

∠Q = 115

∠R = 115

6)

∠B = 120

∠C = 120

7) x = 8

8) EF = 8 and LF = 6

9) the length of altitude is 24, option d is correct.

10) length of altitude BE = 15

11) the length of AB is 8.4, option c is correct.

12) 

x = 35

∠BAD = 70 degree