Worksheet: Isosceles Trapezoids

In this worksheet, we will practice identifying an isosceles trapezoid and using its properties to solve word problems.

Q1:

Choose the option that makes this sentence true: A trapezoid have exactly one pair of congruent sides.

  • Awill always
  • Bcan
  • Ccan never

Q2:

How many trapeziums can you count?

Q3:

The figure shows an isosceles trapezoid. Given that 𝐹𝐾=9 and 𝐽𝐺=26, find 𝐾𝐻.

Q4:

Which statement is true for the given trapezoid?

  • AThe trapezoid has three obtuse angles.
  • BThe trapezoid has two pairs of perpendicular sides.
  • CThe trapezoid has two right angles.
  • DThe trapezoid has two pairs of parallel sides.
  • EThe trapezoid has two acute angles.

Q5:

The speaker shown is an isosceles trapezoid. If 𝑚𝐹𝐽𝐻=82, find 𝑚𝐹𝐺𝐻.

Q6:

Given that 𝐽𝐾𝐿𝑀 is a trapezoid and 𝑚𝑀=68, find 𝑚𝐾.

Q7:

Given that 𝐴𝐵𝐶𝐷 is a trapezoid and 𝑚𝐵𝐶𝐷=101, find 𝑚𝐷.

Q8:

A frame is to be constructed in the shape of a regular trapezoid with a perimeter of 50 inches and a height of 8 inches, where both of the nonparallel sides have a length of 10 inches. Work out the lengths of the two parallel sides.

  • A5 and 25 inches
  • B9 and 21 inches
  • C15 and 15 inches
  • D12 and 28 inches
  • E20 and 20 inches

Q9:

Given that Jennifer is cutting a piece of fabric, where the top of the piece measures 2 ft, the bottom measures 3 ft, and each side measures 4 ft, determine the shape she is cutting the fabric.

  • Aa cube
  • Ba parallelogram
  • Ca triangle
  • Da rectangle
  • Ea trapezoid

Q10:

𝐴 𝐵 𝐶 𝐷 is an isosceles trapezium where 𝐴𝐵=𝐴𝐷=𝐷𝐶=8cm and 𝐵𝐶=16cm. Find the area giving the answer to two decimal places.

Q11:

Find the area of an isosceles trapezium 𝐴𝐵𝐶𝐷, given 𝐴𝐵=𝐴𝐷=𝐷𝐶=3cm and 𝐵𝐶=5cm. Give the answer to one decimal place.

Q12:

An isosceles trapezium of area 74 is divided into two symmetrical pieces by its line of symmetry. What is the area of each piece?

  • A18.5
  • B148
  • C74
  • D37
  • E55.5

Q13:

If 𝐸𝐵𝑀𝐿 is an isosceles trapezium, then which of the following is true?

  • A 𝐿 𝐸 = 𝐿 𝐵
  • B 𝑀 𝐸 = 𝑀 𝐵
  • C 𝐿 𝑀 = 𝐸 𝐵
  • D 𝑀 𝐸 = 𝐿 𝐵
  • E 𝐿 𝐺 = 𝐺 𝐵

Q14:

The figure shows an isosceles trapezoid. Given that 𝐹𝐾=8 and 𝐽𝐺=27, find 𝐾𝐻.

Q15:

The figure shows an isosceles trapezoid. Given that 𝐹𝐾=8 and 𝐽𝐺=23, find 𝐾𝐻.

Q16:

Given that 𝐴𝐵𝐶𝐷 is a trapezoid and 𝑚𝐵𝐶𝐷=122, find 𝑚𝐷.

Q17:

Given that 𝐽𝐾𝐿𝑀 is a trapezoid and 𝑚𝑀=63, find 𝑚𝐾.

Q18:

The speaker shown is an isosceles trapezoid. If 𝑚𝐹𝐽𝐻=75, find 𝑚𝐹𝐺𝐻.

Q19:

The speaker shown is an isosceles trapezoid. If 𝑚𝐹𝐽𝐻=68, find 𝑚𝐹𝐺𝐻.

Q20:

Given that 𝑊𝑋𝑌𝑍 is a trapezoid, 𝑍𝑋=10, and 𝑇𝑌=7, find 𝑊𝑇.

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