Understanding Similar Polygons and Proportional Relationships
Learn about similar polygons, congruent figures, and how to find missing lengths in geometric shapes using proportions. Explore examples and solve for unknown sides in similar figures.
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Presentation Transcript
What are similar polygons? Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional.
Congruent Figures In order to be congruent, two figures must be the same size and same shape. ~ =
Similar Figures Similar figures must be the same shape, but their sizes may be different. ~
Angles and Sides in Similar Polygons Angles A E B F C G Sides AB ~ EF AC ~ EG BC ~ FG A ABC ~ EFG E B C F G
You can find the missing length of a side in a pair of similar figures, by using proportions RST ~ UVW R U x ft. 6 ft. S T W V 35 ft. 7 ft. 6 6 x 7 7 35 x = 30 feet =
Solve for x. 40 in. 30 in.. 12 in. x in. x x 12 30 30 40 x = 9 inches =
Solve for x. Round to the nearest tenth. 12 in. 4 in. 20 in. x in.. 4 4 12 x x 20 x = 6.7 inches =
Solve for x. x 25 m. 14 m. 7 m. 7 7 14 25 25 x x = 50 meters =
Solve for x. Round to the nearest tenth. 17 in. x 35 in. 15 in. 15 15 35 x x 17 x = 7.3 inches =
Determine the missing sides of the triangle 39 in ? in 33 in ? in 8 in 24 in
Determine the length of the missing side Two rectangles are similar. The first is 4 in. wide and 15 in. long. The second is 9 in. wide. Find the length of the second rectangle.
Determine the length of the missing side Two rectangles are similar. One is 5 cm by 12 cm. The longer side of the second rectangle is 8 cm greater than twice the shorter side. Find its length and width.
Similar Figures Which of the following is not a characteristic of similar figures? A. Proportional sides B. Equal angle measurements C. Same shape D. Congruent side lengths
Similar Figures Are the figures below similar? Explain.
Similar Figures Are the figures below similar? Explain.
