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MWA10 6.2 Similar Polygons

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MWA10 6.2 Similar Polygons

MWA10 6.2 Similar Polygons

MWA10 6.2 Similar Polygons

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MWA10 6.2 Similar Polygons

1. 1. Determining if Two Polygons are Similar Slide 1 Two figures are similar if: (1) Corresponding angles are congruent (2) Corresponding sides are proportional B A C D 110 70 4 cm 2 cm 6 cm 7 cm E F G H 110 70 8 cm 14 cm 4 cm 12 cm
2. 2. Determining if Two Polygons are Similar Slide 2 Two figures are similar if: (1) Corresponding angles are congruent (2) Corresponding sides are proportional B A C D 110 70 4 cm 2 cm 6 cm 7 cm E F G H 110 70 8 cm 14 cm 4 cm 12 cm A and E A = E = 110 B and F B = F = 90 C and G C = G = 90 D and H D = H = 70
3. 3. Determining if Two Polygons are Similar Slide 3 Two figures are similar if: (1) Corresponding angles are congruent (2) Corresponding sides are proportional B A C D 110 70 4 cm 2 cm 6 cm 7 cm E F G H 110 70 8 cm 14 cm 4 cm 12 cm 2 1 4 2 AB cm EF cm   6 1 12 2 BC cm FG cm   4 1 8 2 CD cm GH cm   7 1 14 2 DA cm HE cm   Since the corresponding angles are congruent AND the ratio of the corresponding sides equal, the polygons are similar. ABCD ~ EFGH A and E A = E = 110 B and F B = F = 90 C and G C = G = 90 D and H D = H = 70
4. 4. Slide 4 Example 1: Lorinda wants to resize a photo for her scrapbook. She has space for a photo that is 5cm by 8cm. Will the two photos be similar? Original photo – 10cm by 15cm
5. 5. Sketch diagram Slide 5 Example 1: Lorinda wants to resize a photo for her scrapbook. She has space for a photo that is 5cm by 8cm. Will the two photos be similar? Original photo – 10cm by 15cm original resized 15 10 5 8
6. 6. Sketch diagram Slide 6 Example 1: Lorinda wants to resize a photo for her scrapbook. She has space for a photo that is 5cm by 8cm. Will the two photos be similar? Original photo – 10cm by 15cm original resized 15 10 5 8 Calculate ratio of corresponding sides 10 2 5 original new   15 1.875 8 original new   Answer: The two photos will not be similar because the ratios of the corresponding sides are not equal.Are the ratios the same? No
7. 7. Slide 7 Example 2: Aidan frames a 24-inch by 36-inch picture with a 4-inch frame. Is the framed picture similar in shape to the unframed picture?
8. 8. Since the unframed picture and the framed picture are both rectangles, we know that every angle measures 90  Corresponding angles are congruent Slide 8 Example 2: Aidan frames a 24-inch by 36-inch picture with a 4-inch frame. Is the framed picture similar in shape to the unframed picture?
9. 9. Since the unframed picture and the framed picture are both rectangles, we know that every angle measures 90  Corresponding angles are congruent Slide 9 Example 2: Aidan frames a 24-inch by 36-inch picture with a 4-inch frame. Is the framed picture similar in shape to the unframed picture? Answer: While the corresponding angles are congruent, the ratios of the corresponding sides are not equal. The unframed picture and the framed picture are NOT similar. Now to compare ratio of corresponding sides. 4 4 4 4 24 36 24 36 unframed unframed 32 44 24 3 36 4  32 9 44 11  3 9 4 11 
10. 10. Slide 10 Example 3: The scale on a map is 2.5 cm : 500 m. (a) What distance is represented by a 12.5 cm segment on the map? (b) How long would a segment on the map be if it represented 1.5 km?
11. 11. Slide 11 Example 3: The scale on a map is 2.5 cm : 500 m. (a) What distance is represented by a 12.5 cm segment on the map? (b) How long would a segment on the map be if it represented 1.5 km? a) Let x = distance 2.5 ( ) 12.5 500 ( ) cm map cm m distance x  2.5 6250x cm cm m  2.5 6250 2.5 2.5 x cm cm c m cm m   2500x m (a) A 12.5 cm segment on a map will represent a distance of 2500 m.
12. 12. Slide 12 Example 3: The scale on a map is 2.5 cm : 500 m. (a) What distance is represented by a 12.5 cm segment on the map? (b) How long would a segment on the map be if it represented 1.5 km? a) Let x = distance 2.5 ( ) 12.5 500 ( ) cm map cm m distance x  2.5 6250x cm cm m  2.5 6250 2.5 2.5 x cm cm c m cm m   2500x m (a) A 12.5 cm segment on a map will represent a distance of 2500 m. a) Let x = segment 2.5 ( ) 500 ( ) 1500 cm map x m distance m  3750 500cm m x m  500 5 3750 0 5 0 0 0 m m cm m x m  7.5x cm (b) The 1.5 km distance will be a 7.5 cm segment.