Lesson: Inequalities in Two Triangles

In this lesson, we will learn how to use the hinge theorem and its converse in triangles to find the possible range of a side length or angle in two triangles.

Sample Question Videos

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Worksheet: 8 Questions • 3 Videos

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 ?

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 .

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