1 / 15

Solving Proportional Problems with Similar Figures

Learn how to use proportions and cross-multiplication to solve problems involving similar figures. Understand the concept of similar corresponding sides and angles. Includes examples and step-by-step explanations.

kristenk
Download Presentation

Solving Proportional Problems with Similar Figures

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. California Standards Preparation for NS1.3 Use proportions to solve problems (e.g., determine the value of N if = , find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. N 21 4 7

  2. Vocabulary Similar corresponding sides corresponding angles Figures with the same shape but not necessarily the same size. Two figures are similar if; the measures of their corresponding angles are equal and the ratios of the lengths of the corresponding sides are proportional. Sides of two or more polygons that are in the same relative position. Angles of two or more polygons that are in the same relative position.

  3. Similarfigures have the same shape but not necessarily the same size. The symbol ~ means “is similar to.” Corresponding angles of two or more polygons are in the same relative position. Correspondingsidesof two or more figures are between corresponding angles.

  4. E 16 in 28 in AB corresponds to DE. D AC corresponds to DF. 40 in F BC corresponds to EF. ? ? ? ? ? ? = = = = = = Example 1: Determining Whether Two Triangles Are Similar Tell whether the triangles are similar. The corresponding angles of the figures have equal measures. 10 in A C 4 in 7 in B AB DE BC EF AC DF Write ratios using the corresponding sides. 4 16 10 40 7 28 Substitute the length of the sides. 1 4 1 4 1 4 Simplify each ratio. Since the measures of the corresponding sides are equivalent, the triangles are similar.

  5. Writing Math When naming similar figures, list the letters of the corresponding angles in the same order.

  6. For triangles, if the corresponding side lengths are all proportional, then the corresponding angles must have equal measures. For figures that have four or more sides, if the corresponding side lengths are all proportional, then the corresponding angles may or may not have equal measures.

  7. Example 2: Determining Whether Two Four-Sided Figures are Similar Tell whether the figures are similar. The corresponding angles of the figures have equal measure. Write each set of corresponding sides as a ratio.

  8. MN corresponds to QR. NO corresponds to RS. OP corresponds to ST. MP corresponds to QT. Example 2 Continued MN QR NO RS OP ST MP QT

  9. ? ? ? ? ? ? OP ST MN QR NO RS MP QT = = = = = = 8 12 6 9 4 6 10 15 2 3 2 3 2 3 2 3 = = = Example 2 Continued Determine whether the ratios of the lengths of the corresponding sides are proportional. Write ratios using corresponding sides. Substitute the length of the sides. Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the figures are similar.

  10. Reading Math A side of a figure can be named by its endpoints, with a bar above. AB Without the bar, the letters indicate the length of the side.

  11. E 9 in 21 in AB corresponds to DE. D AC corresponds toDF. 27 in F BC corresponds to EF. ? ? ? ? ? ? = = = = = = Check It Out! Example 1 Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar. The corresponding angles of the figures have equal measures. 9 in A C 3 in 7 in B AB DE BC EF AC DF Write ratios using the corresponding sides. 3 9 7 21 9 27 Substitute the length of the sides. 1 3 1 3 1 3 Simplify each ratio. Since the measures of the corresponding sides are equivalent, the triangles are similar.

  12. M P 100 m 80° 65° 60 m 47.5 m 125° 90° O 80 m N Q T 400 m 80° 65° 240 m 190 m 125° 90° S R 320 m Check It Out! Example 2 Tell whether the figures are similar. The corresponding angles of the figures have equal measure. Write each set of corresponding sides as a ratio.

  13. M P 100 m 80° 65° MN corresponds to QR. 60 m 47.5 m 125° 90° O NO corresponds to RS. 80 m N Q T 400 m OP corresponds to ST. 80° 65° MP corresponds to QT. 240 m 190 m 125° 90° S R 320 m Check It Out! Example 2 Continued MN QR NO RS OP ST MP QT

  14. M P 100 m 80° 65° ? ? ? ? ? ? OP ST MN QR NO RS MP QT 60 m = = = 47.5 m = = = 125° 90° O 80 m N 80 320 60 240 47.5 190 100 400 Q T 400 m 80° 65° 1 4 1 4 1 4 1 4 = = = 240 m 190 m 125° 90° S R 320 m Check It Out! Example 2 Continued Determine whether the ratios of the lengths of the corresponding sides are proportional. Write ratios using corresponding sides. Substitute the length of the sides. Since the measure of the corresponding angles are equal and the ratios of the corresponding sides are equivalent, the figures are similar. Simplify each ratio.

More Related