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Worksheet: Hinge Theorem

Q1:

Consider the following two triangles.

Length π‘Ž is congruent to 𝑑 and length 𝑏 is congruent to 𝑒 . Given that πœ™ is greater than πœƒ , what does the hinge theorem tell us about the lengths 𝑐 and 𝑓 ?

  • A 𝑓 and 𝑐 are equal.
  • B 𝑓 is less than 𝑐 .
  • C There is no relation between 𝑓 and 𝑐 .
  • D 𝑓 is greater than 𝑐 .

Q2:

Given that 𝐢 𝐸 = 5 π‘₯ βˆ’ 1 1 and 𝐢 𝐡 = 9 , find the range of all possible values of π‘₯ using the Hinge theorem.

  • A 1 1 5 ≀ π‘₯ < 4
  • B 1 1 5 ≀ π‘₯ ≀ 4
  • C βˆ’ 1 1 5 ≀ π‘₯ ≀ 4
  • D 1 1 5 < π‘₯ < 4
  • E βˆ’ 1 1 5 < π‘₯ < 4

Q3:

In the figure, π‘š ∠ 𝑋 𝑍 π‘Š = ( π‘Ž + 2 0 ) ∘ . Use the hinge theorem to find the range of all possible values of π‘Ž .

  • A 2 2 < π‘Ž < 2 0 0
  • B 6 2 < π‘Ž < 1 6 0
  • C 6 2 < π‘Ž < 2 0 0
  • D 2 2 < π‘Ž < 1 6 0

Q4:

Consider triangles and in the figure.

Without completing any calculations, use the hinge theorem to determine whether is greater than, less than, or equal to .

  • A and are equal.
  • B is less than .
  • C is greater than .

Q5:

Given that π‘š ∠ 𝐴 𝐢 𝐷 = ( 6 π‘₯ βˆ’ 1 2 ) ∘ , use the hinge theorem to find the range of all possible values of π‘₯ in the figure.

  • A 2 < π‘₯ < 7
  • B 2 ≀ π‘₯ ≀ 1 1
  • C βˆ’ 2 < π‘₯ < 7
  • D 2 < π‘₯ < 1 1
  • E βˆ’ 2 ≀ π‘₯ ≀ 7