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.
Q1:
Consider the following two triangles.
Length 𝑎 is congruent to 𝑑 and length 𝑏 is congruent to 𝑒. Given that 𝜙 is greater than 𝜃, what does the hinge theorem tell us about the lengths 𝑐 and 𝑓?
Q2:
Given that 𝑚∠𝐴𝐶𝐷=(6𝑥−12)∘, use the hinge theorem to find the range of all possible values of 𝑥 in the figure.
Q3:
Consider triangles 𝐴𝐵𝐶 and 𝐷𝐸𝐹 in the figure.
Without completing any calculations, use the hinge theorem to determine whether 𝐷𝐹 is greater than, less than, or equal to 𝐴𝐶.
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