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Similar Triangles

Similar Triangles. When are triangles considered similar?. Triangles are similar when: their corresponding angles are equal Their corresponding sides are in proportion to each other They have the same shape, but are different sizes. What are corresponding angles?.

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Similar Triangles

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  1. Similar Triangles

  2. When are triangles considered similar? • Triangles are similar when: • their corresponding angles are equal • Their corresponding sides are in proportion to each other • They have the same shape, but are different sizes

  3. What are corresponding angles? • Angles that correspond to each other are in the same relative position in similar triangles. • In the two triangles below, <K = <H, <L = <I and <M = <J

  4. Don’t be fooled! • Be careful: triangles can be reversed in position – look carefully for the corresponding angles: r l ftm n • Can you name the corresponding angles???

  5. Don’t be fooled! • Sometimes, triangles can be flipped and reversed! Can you still find the corresponding angles?

  6. Don’t be fooled! • Sometimes, similar triangles can be hiding inside of each other. Can you still find the corresponding angles?

  7. What are corresponding sides? • In the triangles below, the corresponding sides are the ones that are connecting the corresponding angles. They are in proportion to each other and have the same relative position. • So, ~ and ~ and ML ~

  8. Corresponding sides • In similar triangles, corresponding sides are proportional. That means that they have been either enlarged or reduced by the same scale factor. • By what scale factor have the corresponding sides been reduced in the triangles below?

  9. Corresponding sides • You can find missing side lengths in corresponding sides by setting up a ratio or proportion to solve: • = • By cross multiplying, x = 9

  10. Homework: • Page 150 - 151 • #1, 2, 4, 5, 6, 7, 9, 10, 11

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