Unit 2, Lesson 17
Finding All the Unknown Values in Triangles
Integrated Math 2
17.1
Warm-up
Which three go together? Why do they go together?
A
B
C
D
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Which three go together? Why do they go together?
A
B
C
D
Triangle is similar to triangle . Give reasonable measurements for all 3 sides of triangle . Explain your reasoning.
We have multiple strategies to find unknown side lengths in similar right triangles.
Two right triangles, F G H and A B C. Angles G F H and B A C are marked congruent, Angles F G H and A B C are marked right angles. Side F G labeled y, Side G H labeled 12 over 5, Side F H labeled 4. Side A B labeled 4, side B C labeled 3, Side C A labeled 5.
Because triangle is a right triangle, . Because triangle is a right triangle, . Because triangle is similar to triangle , there are many equations to write using proportional relationships. We can use any combination of these equations to solve for and .
By similarity, . Substituting into the Pythagorean Theorem gives which is true.
By the Pythagorean Theorem, , so . By similarity , which also equals 3.