Lesson Worksheet: Inequalities in Two Triangles Mathematics
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.
Given that , use the hinge theorem to find the range of all possible values of in the figure.
Given that and , find the range of all possible values of using the Hinge theorem.
In the figure, . Use the hinge theorem to find the range of all possible values of .
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 .
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 .
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 .