Lesson Menu Main Idea and New Vocabulary NGSSS Key Concept:Similar Polygons Example 1:Identify Similar Polygons Example 2:Find Missing Measures Key Concept:Ratios of Similar Figures Example 3:Find Perimeter Five-Minute Check

Main Idea/Vocabulary Identify similar polygons and find missing measures of similar polygons. similar polygons corresponding parts scale factor

NGSSS MA.8.G.2.1 Use similar triangles to solve problems that include height and distances.

Key Concept

Example 1 Identify Similar Polygons Determine whether triangle DEF is similar to triangle HJK. Explain. First, check to see if corresponding angles are congruent.  D   H,  E   J, and  F   K, so all corresponding angles are congruent.

Example 1 Next, check to see if corresponding sides are proportional. Identify Similar Polygons Answer: Therefore, the triangles are similar. Since, the corresponding sides are proportional.

Example 1 CYP A.Yes; corresponding angles are congruent and corresponding sides are proportional. B.Yes; corresponding angles are congruent and corresponding sides are congruent. C.No; corresponding angles are congruent, but corresponding sides are not proportional. D.No; corresponding angles are congruent, but corresponding sides are not congruent. Determine whether the figures are similar. Explain.

Example 2 GEOMETRY Given that rectangle LMNO ~ rectangle GHIJ, find the missing measure. Find Missing Measures Find the scale factor from rectangle LMNO to rectangle GHIJ. scale factor:

Example 2 Find Missing Measures So, a length on rectangle LMNO is times as long as the corresponding length on rectangle GHIJ. Let m represent the measure of ON. Write the equation. m = 6Multiply. Answer: m = 6

Example 2 CYP A.6 B.8 C.10 D.12 GEOMETRY Given that quadrilateral KLMN ~ quadrilateral RSTU, find the missing measure.

Key Concept 3

Example 3 Find Perimeter BILLBOARDS A model of a billboard has a side length of 3 inches. The corresponding side on the actual billboard is 4 feet long. The model has a perimeter of 42 inches. What is the perimeter of the actual billboard? Step 1The actual length is proportional to the length of the model with a ratio of. Find the scale factor. Convert feet to inches and divide out units.

Example 3 Step 2 Find the perimeter of the actual billboard. P = or 672 Substitute. Then simplify. Find Perimeter Answer: The perimeter of the actual billboard is 672 inches or 56 feet. perimeter of billboard = perimeter of model scale factor

Example 3 CYP A.4 feet B.4.5 feet C.9 feet D.18 feet PHOTOGRAPHS A photograph has a side length of 8 inches. The photo is enlarged to poster size and the corresponding side on the poster is 2 feet long. The photograph has a perimeter of 36 inches. What is the perimeter of the poster?

A.Yes; corresponding sides are proportional. B.Yes; corresponding sides are congruent. C.No; corresponding sides are not congruent. D.No; corresponding sides are not proportional. Five Minute Check 1 Determine whether the pair of polygons is similar. Explain.

The pair of polygons is similar. Find the missing side measure. Five Minute Check 2 A. B. C. D.

A.C. B.D. A greeting card is 8 inches by 6 inches, but it will have to be cut to fit in an envelope. The scale factor from the original card to the smaller card is 5:4. Find the dimensions of the smaller card. Five Minute Check 3