# Worksheet: Inequalities in Two Triangles

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.

Q1:

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 .

Q2:

Given that , use the hinge theorem to find the range of all possible values of in the figure. • A
• B
• C
• D
• E

Q3:

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

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 .