# 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.

**Q2: **

Given that , use the hinge theorem to find the range of all possible values of in the figure.

- A
- B
- C
- D
- E

**Q4: **

Given that and , find the range of all possible values of using the Hinge theorem.

- A
- B
- C
- D
- E

**Q5: **

In the figure, . Use the hinge theorem to find the range of all possible values of .

- A
- B
- C
- D
- E

**Q6: **

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 .

**Q7: **

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 .

**Q8: **

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 .