Identifying Similar Shapes using Ratios
Discover how to determine if shapes are similar based on ratios of their side lengths. Explore various pairs of shapes and triangles to understand the concept of similarity.
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Presentation Transcript
Which of these pairs of shapes do you think are similar? Same width, different lengths. Different interior angles.
These are pairs of similar triangles. Not to scale. What is the Scale Factor of Enlargement for each pair? Scale Factor = 3 Scale Factor = 2 6 cm 3 cm 2 cm 3 cm 6 cm 6 cm Scale Factor = 4 12 cm Scale Factor = 1.5 4 cm 3 cm 6 cm
Working with ratio can show that two shapes are similar 35 cm 28 cm 12 cm 15 cm 12 : 28 15 : 35 3 : 7 3 : 7 Similar shapes will have their side lengths in the same ratio.
Are these shapes similar? 21 cm 18 cm 7 cm 6 cm 30 cm 35 cm 6 : 18 : 30 7 : 21 : 35 1 : 3 : 5 1 : 3 : 5 Similar shapes will have their side lengths in the same ratio.
Are these shapes similar? 17.5 cm 10.5 cm 15 cm 9 cm 18 cm 21 cm 10.5 : 17.5 : 21 21 : 35 : 42 9 : 15 : 18 3 : 5 : 6 3 : 5 : 6 Similar shapes will have their side lengths in the same ratio.
Are these triangles similar? Use ratios to prove it 6 cm 6 cm 10 cm 10 cm 3 cm 5 cm 3 : 6 : 6 5 : 10 : 10 1 : 2 : 2 1 : 2 : 2 Not to scale.
Are these triangles similar? Use ratios to prove it 25 cm 10 cm 30 cm 30 cm 12 cm 34 cm 10 : 25 : 30 12 : 30 : 34 2 : 5 : 6 6 : 15 : 17 Not to scale.
Express side lengths as ratios to check whether these pairs of shapes are similar. 4 cm 6 cm 14 cm 5 cm 7.5 cm 2 : 3 18 cm 3 : 4 A B 4 : 5 5.4 cm 17.5 cm 5 cm 10.8 cm 9.6 cm 44 cm 25 cm 16.2 cm 14.4 cm 60 cm 2:7:10 3.6 cm 12 cm C D 3:8:9 3:11:15
Not to scale. Which of these triangles are similar to each other? 6 cm Each triangle is drawn at a different scale. 2.5 cm Express the side-length of each triangle as a ratio & simplify. Similar triangles will have the same ratio of side lengths! 2 cm 9 cm 6 cm 8 cm 4 cm 9 cm 9 cm 1.5 cm 6 cm 5 cm 12 cm 3 cm 4 cm 3 cm 10 cm 7.5 cm 4 cm 6 cm 8 cm 4 cm 12 cm 8 cm 6 cm 10 cm 4 cm 10 cm 1.5 cm 12 cm 1 cm 6 cm 10 cm 2 cm 5 cm 10 cm 10 cm 6 cm 4 cm 12.5 cm 10 cm 10 cm 15 cm 8 cm 6 cm 6 cm 14 cm 3.5 cm 6 cm 12 cm 17.5 cm
Not to scale. Which of these triangles are similar to each other? 6 cm Each triangle is drawn at a different scale. 2.5 cm 2:3:3 Express the side-length of each triangle as a ratio & simplify. Similar triangles will have the same ratio of side lengths! 3:4:5 2 cm 9 cm 6 cm 8 cm 4 cm 9 cm 9 cm 1.5 cm 2:3:4 2:3:4 3:4:5 6 cm 5 cm 12 cm 3 cm 4 cm 3 cm 10 cm 7.5 cm 4 cm 6 cm 2:4:5 8 cm 4 cm 12 cm 8 cm 6 cm 10 cm 4 cm 2:3:3 2:5:5 2:3:3 10 cm 1.5 cm 12 cm 1 cm 2:3:4 6 cm 10 cm 2 cm 5 cm 10 cm 2:3:5 2:4:5 10 cm 6 cm 4 cm 12.5 cm 10 cm 3:5:5 10 cm 15 cm 3:4:5 8 cm 6 cm 2:4:5 6 cm 14 cm 3.5 cm 1:4:5 6 cm 12 cm 17.5 cm
Show me Three similar right angled triangles with perpendicular lengths in the ratio 1 : 2.5
