Mod 16.3: Corresponding Parts of Similar Figures

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Mod 16.3: Corresponding Parts of Similar Figures Essential Question: If two figures are similar, what can you determine about measures of corresponding angles and lengths? CASS: G-SRT.2 Similarity. MP.4 Modeling

Essential Question: If two figures are similar, what can you determine about measures of corresponding angles and lengths?

EXPLORE 1 p. 851

EXPLORE 1 p. 851

EXPLORE 1 p. 852

EXPLAIN 1 p. 853 Two figures that can be mapped to each other by similarity transformations (dilations and rigid motions) are similar. Similar figures have certain properties.

Vocabulary similar polygons: Two polygons are similar, the side lengths are proportional and the angle measures are equal. A D F G The symbol for similar is ~ E H

EXAMPLE 1 p. 853 JN L U VW

REFLECT p. 854 4. If you know two figures are similar, what angle or side measurements must you know to find the dilation used in the transformations mapping one figure to another? You must know measurements of one pair of corresponding sides to find the scale factor.

Your Turn p. 854 5. Triangles △PQR and △LMN are similar. If QR = 6 and MN = 9, what similarity transformation (in coordinate notation) maps △PQR to △LMN? No. No, the proportion must compare corresponding sides.

EXPLAIN 2 p. 854, Example A Find the value of x and y. Hint: Rotate polygon PQRS clockwise by 45° to see similarity. x = 17 y = 5

EXPLAIN 2 p. 854, Example B Find the value of x and y. Hint: Rotate figures and write similarity statement. JKLMN ~ VWXYZ

EXPLAIN 2 p. 854, Example B Find the value of x and y. JKLMN ~ VWXYZ

REFLECT 7. Discussion: What are some things you need to be careful about when solving problems involving finding the values of variables in similar figures? Set up side lengths proportion correctly. Side lengths are proportional rather than equal. Errors in the calculations.

Your Turn p. 855 Use the diagram, in which △ABE ∼ △ACD. 8. Find the value of x. 9. Find the value of y

ELABORATE p. 855 Similar figures have corresponding angles that are congruent and have corresponding sides that are proportional.

Essential Question: If two figures are similar, what can you determine about measures of corresponding angles and lengths? EQ Answer: Similar figures have corresponding angles that are congruent and have corresponding sides that are proportional.