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Understanding Similar Polygons and Proportions in Geometry

This resource explores the concept of proportions in geometry, explaining how they indicate equality between two ratios. It covers the symbol for 'is similar to' (~) and how to use proportions to find the lengths of sides in similar figures. Additionally, the relationship between map scales and actual distances is highlighted, demonstrating practical applications of geometry in real-life scenarios such as travel. The text includes examples of congruent angles, similarity correspondence, and exercises to reinforce comprehension.

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Understanding Similar Polygons and Proportions in Geometry

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Presentation Transcript

  1. 7-1B Similar Polygons What is a proportion? What are proportions used for in Geometry? What Geometry symbol is used for “is similar to”? What similar figure is used for travel?

  2. Definition • Proportion--an equation stating that two ratios are equal.

  3. Geometry Symbols The symbol ~ means “is similar to”. The order of the letters in the similarity correspondence indicates the corresponding parts. ABC ~ XYZ

  4. ABCDE ~ MNOPQ. Name all pairs of congruent corresponding angles, and write proportions using the pairs of corresponding sides. N O E A D M P C B Q

  5. Write the similarity correspondence. Name all pairs of congruent corresponding angles and write proportions using the pairs of corresponding sides. I 45 Q R 15 X F Y 53° 5 10 75 25 60 20 6 3 V W 37° 30 E 4 G T 90 S J H 8

  6. Map Reading The scale on a map relates the size of an object on the map to its actual size. Where do you find the scale on a map? Use the scale and algebra to find the distance between Mishawaka and Kokomo.

  7. Given: FGHJ~WXYZFind YZ W Z Since the length of the corresponding sides are proportional, set up a proportional statement. J 12 F 9 X G 14 H Y

  8. EFGH ~ KNML • Find the measures of angles E, G, and N. • Find x, y, and z. • What is the similarity ratio of KNML to EFGH? N F X 43° 10 35 E 4 143° z G K H 6 67° 10 107° L y M x = 14, y = 15, z = 25 5/2

  9. What is a proportion? A proportion is an equation stating that two ratios are equal. • What are proportions used for in Geometry? To find the length of the sides of similar figures. • What Geometry symbol is used for “is similar to”? ~ • What similar figure is used for travel? Maps

  10. Assignment 7-1B p. 471, 1-8, 11-13, 28-33

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