Geometry: An Interactive Journey to Mastery

Lesson 10: Practical Applications of Similarity

Practical Applications of Similarity

Lesson 10

Topics

x The SSS similarity principle for triangles.

x The converse of the Pythagorean theorem.

x Applications of similarity and congruence principles.

Results

x SSS principle: If two triangles have three sides that match in the

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That is, the three angles of the triangles match as well.

x Pythagorean converse: If a triangle has three sides of lengths p, q, and r satisfying p^2 + q^2 = r^2 , then the

triangle is a right triangle with the side of length r the hypotenuse.

Summary

In this lesson, we explore one more similarity principle for triangles, the SSS principle, and show how it follows

as a logical consequence of the SAS and AA similarity principles. This allows us to establish the converse of the

Pythagorean theorem. We also explore a number of practical applications of the three similarity principles.

Example 1

How many essentially different triangles can you make with 3 sticks, one of length 11 inches, one of length 15

inches, and a third of length 20 inches?

Solution

Just one. Any two triangles with these side lengths must be congruent by the SSS principle.

a c

b

ka

kb

kc

Figure 10.1