Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion...

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Similar Polygons Similar Polygons 8.2 8.2

Transcript of Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion...

Page 1: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

Similar Polygons 8.2Similar Polygons 8.2

Page 2: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

• Define similar polygons.

• Name polygons.

homeworkhomework

• Learn the proportion properties.

• Find the missing measure in proportional figures.

Page 3: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

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

Page 4: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.
Page 5: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.
Page 6: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

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

Page 7: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

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

Page 8: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

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

Page 9: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

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.

Page 10: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

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

Page 11: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

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

LP

AE

OP

DE

NO

CD

MN

BC

LM

AB

Page 12: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

Ryan is designing a new menu for the restaurant Ryan is designing a new menu for the restaurant where he works. Determine whether the size for the where he works. Determine whether the size for the new menu is similar to the original menu. If so, write new menu is similar to the original menu. If so, write the similarity statement and scale factor. Explain the similarity statement and scale factor. Explain your reasoning.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, Since corresponding sides are not proportional, ABCDABCD is not is not similar to similar to FGHKFGHK. So, the menus are not similar.. So, the menus are not similar.

Page 13: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

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:

Compare corresponding angles.

Since all angles of a rectangle are right angles and right angles are congruent, corresponding angles are congruent.

Compare corresponding sides.

__45

Since corresponding sides are proportional, Since corresponding sides are proportional, ABCDABCD ~ ~ RSTURSTU. . So the menus are similar with a scale factor of .So the menus are similar with a scale factor of .

R S

TU

Page 14: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

The two polygons are similar. Find x and y.Use the congruent angles to write the corresponding vertices in order.

polygon ABCDE ~ polygon RSTUV

UVDE

RSAB

1y

8

4

6

6(y + 1) = 8(4)

6y + 6 = 32

6y = 26

3

13y

Page 15: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

Identify the pairs of congruent angles and corresponding sides.

B G and C H. By the Third Angles Theorem, A J.

Page 16: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.

rectangles ABCD and EFGH

Identify pairs of congruent angles.

All s of a rect. are rt. s and are .

Compare corresponding sides.

A E, B F, C G, and D H.

Thus the similarity ratio is , and ABCD ~ EFGH.

Page 17: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.

∆PQR and ∆STWIdentify pairs of congruent angles.

isos. ∆

Compare corresponding angles.

Since no pairs of angles are congruent, the triangles are not similar.

72 72

mT = 180° – 2(62°) = 56°

56

P R and S W

62 62

Page 18: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

Identify pairs of congruent angles.

Determine if ∆JLM ~ ∆SPN. If so, write the similarity ratio and a similarity statement.

M N, L P, J S

Compare corresponding sides.

Thus the similarity ratio is , and ∆JLM ~ ∆SPN.

Page 19: Similar Polygons 8.2. Define similar polygons. Name polygons. homework Learn the proportion properties. Find the missing measure in proportional figures.

AssignmentAssignment

Section 11 – 36 Section 11 – 36 Similar Polygons 8.2 oddSimilar Polygons 8.2 odd