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Similar Triangles

Similar Triangles. Information. Proving triangles similar. Triangles are similar when corresponding angles are congruent and corresponding sides have the same ratio. Prove that △ ABC ~ △ DEC. show corresponding angles are congruent:. 19.7. reflexive property of congruence:. .

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Similar Triangles

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  1. Similar Triangles

  2. Information

  3. Proving triangles similar Triangles are similar when corresponding angles are congruent and corresponding sides have the same ratio. Prove that △ABC~△DEC. show corresponding angles are congruent: 19.7 reflexive property of congruence:  ∠BAC≅ ∠DAE 26.3 35.3  corresponding angles postulate: ∠ADE≅ ∠ABC 16.9  ∠AED≅ ∠ACB 28.0 15.6 show corresponding sides have the same ratio:  AD/AB =35.3/(35.3+19.7) = 0.64  DE/BC =16.9/26.3 = 0.64  AE/AC =28.0/(28.0+15.6) = 0.64

  4. Using similarity in triangles

  5. Exploring similarity postulates

  6. Establishing the AA similarity postulate Angle-angle similarity postulate: If two angles of a triangles are congruent to two angles of another triangle, then the two triangles are similar. • If two triangles are similar, they are related by similarity transformations. • Rotation, reflection and transformation preserve angles and side lengths. • Dilation preserves angle but changes the sides lengths proportionally. • If two angles of a triangle are specified, the third one is also determined. • Therefore, two triangles with two congruent angles are similar.

  7. Similar triangles

  8. Satellite photography The camera on the satellite takes a photo of something on Earth. By using similar triangles, can you find the length of the object? image size focal length of camera lens The height above ground is 150km, the image size is 25mm, and the focal length is 100mm. heightabove Earth object size

  9. Summary activity

  10. Surveying

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