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.
Students will be able to
Q1:
Consider the following two triangles.
Length ๐ is congruent to ๐ and length ๐ is congruent to ๐. Given that ๐ is greater than ๐, what does the hinge theorem tell us about the lengths ๐ and ๐?
Q2:
Given that ๐โ ๐ด๐ถ๐ท=(6๐ฅโ12)โ, use the hinge theorem to find the range of all possible values of ๐ฅ in the figure.
Q3:
Consider triangles ๐ด๐ต๐ถ and ๐ท๐ธ๐น in the figure.
Without completing any calculations, use the hinge theorem to determine whether ๐ท๐น is greater than, less than, or equal to ๐ด๐ถ.
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