Similarity: Similar Polygons

Section Warm-Up

In this section, you will need to use some skills you have learned earlier in this class and in previous classes. Complete the warm-up below and ask for help on any problems that you don’t remember how to do.

Think & Click: Section Warm-Up

In the previous lessons, we learned about ratios, proportions and similar triangles. We are going to continue learning about those concepts here. Let’s review some of the concepts we learned to make sure you are ready for this lesson.

Complete the Think & Click activity by looking at each problem below, thinking about it, and then clicking on the question to reveal the solution.

Show that the following triangles are similar. Write a statement about their similarity.

Triangle FLP, with the measure of side FL equal to 16, the measure of side LP equal to 22 and the measure of side PF equal to 18; triangle QMD, with the measure of side QM equal to 16.5, the measure of side MD equal to 13.5, and the measure of side DQ equal to 12

Triangle FLP and triangle QMD

$sixteen-twelfths approximately equals 1 point 33; the fraction 18 over 13 point 5 approximately equals 1 point 33; the fraction 22 over 16 point 5 approximately equals 1 point 33$

All pairs of sides are proportional, so the triangles are similar.

Find the lengths of the missing sides and the measures of the missing angles if triangle ABC is similar to triangle XYZ.

triangle ABC with the measure of side AB equal to 6, the measure of side BC equal to 10, the measure of side AC equal to 8, angle A measures 90 degrees and angle C measures 34 degrees; triangle XYZ with the measure of side XY equals to 3.6 and angle x mearues 90 degrees

Triangle ABC and triangle XYZ

the measure of angle B equals 180 minus 90 minus 34 equals 56 degrees

the measure of angle Y = the measure of angle B equals 56 degrees; the measure of angle Z equals the measure of angle C equals 34 degrees

$the fraction AB over XY equals the fraction BC over YZ; the fraction 6 over 3 point 6 equals the fraction 10 over YZ; 6 YZ equals 36; YZ equals 6$

$the fraction AB over XY equals the fraction AC over XZ; the fraction 6 over 3 point 6 equals the fraction 8 over XZ; 6 XZ equals 28 point 8; XZ equals 4 point 8$

A 6.2 foot tall man is standing by a 150 foot tall building. The building is casting a shadow that is 120 feet long. How long is the man’s shadow?

$the fraction “man” over “building” equals the fraction “man’s shadow” over “building’s shadow”; the fraction 6 point 2 over 150 equals the fraction x over 120; 6 point 2 times 120 equals 150 x; 744 equals 150 x; 4.96 equals x$

The man’s shadow is 4.96 feet long.