Lesson Worksheet: The Hinge Theorem Mathematics • 11th Grade
In this worksheet, we will practice using the hinge theorem and its converse in triangles to find the possible range of a side length or angle in two triangles.
Q2:
In the triangles, using the converse of the hinge theorem, determine whether is greater than, less than, or equal to .
- A is larger than .
- B is equal to .
- C is less than .
Q3:
Consider the two triangles in the diagram.
Length is equal to length and length is equal to length . 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 and ?
- AThe measure of is smaller than the measure of .
- BThe measure of is equal to the measure of .
- CThe measure of is greater than the measure of .
Q4:
Consider the triangles and , where and . Given that and using the converse of the Hinge theorem, determine whether is greater than .
- A is smaller than .
- B is greater than .
- C is equal to .
Q5:
Consider the following two triangles.
Length is congruent to and length is congruent to . Given that is greater than , what does the hinge theorem tell us about the lengths and ?
- A and are equal.
- BThere is no relation between and .
- C is less than .
- D is greater than .
Q6:
Given that and , find the range of all possible values of using the Hinge theorem.
- A
- B
- C
- D
- E
Q7:
In the figure, . Use the hinge theorem to find the range of all possible values of .
- A
- B
- C
- D
- E
Q8:
Given that , use the hinge theorem to find the range of all possible values of in the figure.
- A
- B
- C
- D
- E
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