Similar Figures and Indirect Measurement Math 7 Unit 5

Similar Figures and Indirect Measurement For polygons to be similar, three things must be true. Use the following example to figure out the first one. Are these similar figures? How do you know? No, they are not similar because they are not the same shape.

Similar Figures and Indirect Measurement Use the following example to figure out the next one. They have the same general shape, but what is different about them? Be specific. Remember, you don’t know side lengths, so don’t focus too much on that aspect. Corresponding angles must be congruent (equal).

Similar Figures and Indirect Measurement Now, if we knew side lengths, how could you prove these are not similar mathematically. Corresponding side lengths are not proportional or do not share the same scale factor. 9 9 6 6 10 5

Similar Figures and indirect measurement In order for two shapes to be considered mathematically similar, the following must be true: They have the same general shape Corresponding angles are congruent Corresponding side lengths are proportional or share a common scale factor.

Similar Figures and Indirect Measurement Are these two figures mathematically similar? They have the same general shape 45° 45° 36 Corresponding angles are congruent 27 90° ? 90° 24 18 Corresponding side lengths are proportional. Therefore, the figures are similar.

Similar Figures and Indirect Measurement Are the following figures similar? No, they are not because the corresponding sides are not proportional. 8 ft. 5 ft. 18 ft. 9 ft.

Similar Figures and Indirect Measurement What happens if you know that rectangles ABCD and PQRS are similar. How could we find x? A B Q R P S D C 8 12 6 x Since these ratios are equivalent, one method would be to use a ratio table to find the missing value. multiply by 2 x = 16 multiply by 2

Similar Figures and Indirect Measurement The following figures are similar. Solve for the designated side. 5 3 y 8

Similar Figures and Indirect Measurement The following figures are similar. Solve for the designated side. 5 q 4 6

Similar Figures and Indirect Measurement Knowing what we do about similar figures, how could we apply it to real life? Let’s find out.

Similar Figures and Indirect Measurement A tree stands 12 ft. tall and casts a shadow 8 ft. long. At the same time, a person casts a shadow that is 3 ft. long. To the nearest tenth of a foot, how tall is the person? Draw a picture, set up a proportion and solve. The person is 4 ½ feet tall. x 12 8 3

Similar Figures and indirect measurement This is called indirect measurement. What do you think a good definition would be for indirect measurement? a method of determining length or distance without measuring directly

Similar Figures and Indirect Measurement Laura is 5.5 ft. tall and casts a shadow that is 3.2 ft. long. She is standing next to a flag pole that is 23 ft. tall. To the nearest tenth of a foot how long is the flag pole’s shadow? Draw a picture, set up a proportion and solve. The shadow is about 13.4 ft. long. 23 5.5 f 3.2

Similar Figures and Indirect Measurement A Civil War monument in Charlestown, Massachusetts is 221 ft. tall. It casts a shadow 189 feet long at the same time a nearby tree casts a shadow 29 feet long. To the nearest tenth of a foot, how tall is the tree? The tree is about 33.9 feet tall. 221 a 29 189

Similar Figures and Indirect Measurement Scale Drawing – A drawing that shows a real object with accurate sizes except they have all been reduced or enlarged by a certain amount (called the scale). Example of a scale drawing – Maps Architectural and engineering drawings Charts and pictures in books How does this relate to similar figures? Let’s look.

Similar Figures and Indirect Measurement A map scale is 1 in. = 75 mi. The map distance between two towns is 3.5 in. Find the actual distance between the towns. Set up a proportion and solve. The actual distance is 262.5 miles.

Similar Figures and Indirect Measurement My map scale says that 1 inch = 15 miles. Using the map, I measure the distance remaining on Interstate 40 as about 9 inches. How many miles do I still need to go to get to the beach? The actual distance is 135 miles.

Similar Figures and Indirect Measurement If we still have 135 miles to go and we continue going 60 miles per hour, how long until we get there? It will take us 2 ¼ hours or 2 hours and 15 minutes. ÷60 ÷60