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Worksheet: Properties of Kites

In this worksheet, we will practice using the properties of kites, the Pythagorean theorem, and the polygon interior angles sum theorem to find measures in kites.

Q1:

If π‘Š 𝑋 π‘Œ 𝑍 is a kite, find 𝑍 π‘Œ .

  • A22
  • B17
  • C √ 3 1 4
  • D 1 3 √ 2
  • E √ 7 4

Q2:

If π‘Š 𝑋 π‘Œ 𝑍 is a kite, find 𝑍 π‘Œ .

  • A31
  • B24
  • C25
  • D26
  • E √ 1 4 9

Q3:

If π‘Š 𝑋 π‘Œ 𝑍 is a kite, find 𝑍 π‘Œ .

  • A24
  • B19
  • C √ 3 8 6
  • D √ 3 9 7
  • E √ 6 1

Q4:

Given that 𝐹 𝐺 𝐻 𝐽 is a kite, where π‘š ∠ 𝐹 𝐺 𝐻 = 1 0 8 ∘ and π‘š ∠ 𝐹 𝐽 𝐻 = 6 4 ∘ , find π‘š ∠ 𝐺 𝐹 𝐽 .

Q5:

Chloe wants to design a kite with two diagonals of lengths 46 cm and 78.2 cm. If she wants to join the midpoints of the kite’s sides using a string, how long should the string be?

Q6:

Sophia wants to design a kite with two diagonals of lengths 74 cm and 162.8 cm. If she wants to join the midpoints of the kite’s sides using a string, how long should the string be?

Q7:

Given that 𝐴 𝐡 𝐢 𝐷 is a kite, π‘š ∠ 𝐴 = 1 2 7 ∘ , and π‘š ∠ 𝐷 = 8 6 ∘ , find π‘š ∠ 𝐢 .

Q8:

Given that 𝐴 𝐡 𝐢 𝐷 is a kite, π‘š ∠ 𝐴 = 9 2 ∘ , and π‘š ∠ 𝐷 = 1 0 2 ∘ , find π‘š ∠ 𝐢 .

Q9:

A kite has vertices at the points ( 2 , 0 ) , ( 3 , 2 ) , ( 4 , 0 ) , and ( 3 , βˆ’ 3 ) .

Work out the perimeter of the kite. Give your solution to one decimal place.

Work out the area of the kite.

Q10:

Complete the following: If is a quadrilateral in which and , then is .

  • A equal to
  • B parallel to
  • C congruent to
  • Dthe perpendicular bisector of

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