Worksheet: Inequalities in Two Triangles

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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.

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.

Q5:

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

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 .