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Worksheet: Converse of the Hinge Theorem

Q1:

Consider the two triangles in the diagram.

Length π‘Ž is equal to length 𝑑 and length 𝑏 is equal to length 𝑒 . Given that the perimeter of triangle 1 is less than the perimeter of triangle 2, what does the converse of the hinge theorem tell us about the measures of angles πœƒ and πœ™ ?

  • AThe measure of πœ™ is equal to the measure of πœƒ .
  • BThe measure of πœ™ is smaller than the measure of πœƒ .
  • CThe measure of πœ™ is greater than the measure of πœƒ .

Q2:

In the triangles, using the converse of the hinge theorem, determine whether πœƒ is greater than, less than, or equal to πœ™ .

  • A πœƒ is equal to πœ™ .
  • B πœƒ is larger than πœ™ .
  • C πœƒ is less than πœ™ .

Q3:

Consider the triangles 𝐴 𝐡 𝐢 and 𝐷 𝐸 𝐹 , where 𝐴 𝐡 = 𝐷 𝐸 and 𝐡 𝐢 = 𝐸 𝐹 . Given that 𝐴 𝐢 > 𝐷 𝐹 and using the converse of the Hinge theorem, determine whether ∠ 𝐴 𝐡 𝐢 is greater than ∠ 𝐷 𝐸 𝐹 .

  • A ∠ 𝐴 𝐡 𝐢 is equal to ∠ 𝐷 𝐸 𝐹 .
  • B ∠ 𝐴 𝐡 𝐢 is smaller than ∠ 𝐷 𝐸 𝐹 .
  • C ∠ 𝐴 𝐡 𝐢 is greater than ∠ 𝐷 𝐸 𝐹 .