Similar Polygons 8.2

Define similar polygons. Name polygons. Learn the proportion properties. Find the missing measure in proportional figures. homework

Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional.

Writing a similarity statement is like writing a congruence statement—be sure to list corresponding vertices in the same order. Writing Math When you work with proportions, be sure the ratios compare corresponding measures. Remember

Figures that are similar (~) have the same shape but not necessarily the same size.

If ΔABC ~ ΔRST, list all pairs of congruent angles and write a proportion that relates the corresponding sides. Use the similarity statement. ΔABC ~ ΔRST Congruent Angles: A  R, B  S, C  T

A similarity ratio is the ratio of the lengths of the corresponding sides of two similar polygons. The similarity ratio of ∆ABC to ∆DEF is , or . The similarity ratio of ∆DEF to ∆ABC is , or 2.

Given the proportionality statement for two similar quadrilaterals, write a similarity statement that shows the correct correspondence.

Given pentagon ABCDE ~ pentagon LMNOP, write a proportionality statement for the ratios between the sides.

Original Menu: New Menu: Ryan is designing a new menu for the restaurant where he works. Determine whether the size for the new menu is similar to the original menu. If so, write the similarity statement and scale factor. Explain your reasoning. Original Menu: New Menu: Compare corresponding angles. Since all angles of a rectangle are right angles and right angles are congruent, corresponding angles are congruent. Compare corresponding sides. Since corresponding sides are not proportional, ABCD is not similar to FGHK. So, the menus are not similar.

Original Menu: New Menu: Ryan is designing another menu for the restaurant where he works. Determine whether the size for the new menu is similar to the original menu. If so, write the similarity statement and scale factor. Explain your reasoning. Original Menu: New Menu: R S T U Compare corresponding angles. Since all angles of a rectangle are right angles and right angles are congruent, corresponding angles are congruent. Compare corresponding sides. __ 4 5 Since corresponding sides are proportional, ABCD ~ RSTU. So the menus are similar with a scale factor of .

The two polygons are similar. Find x and y. Use the congruent angles to write the corresponding vertices in order. polygon ABCDE ~ polygon RSTUV 6(y + 1) = 8(4) 6y + 6 = 32 6y = 26

Identify the pairs of congruent angles and corresponding sides. B  G and C  H. By the Third Angles Theorem, A  J. 15

Identify pairs of congruent angles. Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. Identify pairs of congruent angles. All s of a rect. are rt. s and are . rectangles ABCD and EFGH A  E, B  F, C  G, and D  H. Compare corresponding sides. Thus the similarity ratio is , and  ABCD ~  EFGH. 16

Identify pairs of congruent angles. isos. ∆ ∆PQR and ∆STW Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. mT = 180° – 2(62°) = 56° 56 P  R and S  W 62 72 62 Identify pairs of congruent angles. isos. ∆ ∆PQR and ∆STW Compare corresponding angles. Since no pairs of angles are congruent, the triangles are not similar. 17

Determine if ∆JLM ~ ∆SPN Determine if ∆JLM ~ ∆SPN. If so, write the similarity ratio and a similarity statement. Identify pairs of congruent angles. M  N, L  P, J  S Compare corresponding sides. Thus the similarity ratio is , and ∆JLM ~ ∆SPN.

Assignment Section 11 – 36 Similar Polygons 8.2 odd