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Aim: Proving Triangles Similar

Aim: Proving Triangles Similar. By: Michael Shi and Max Fiedziukiewicz. Two triangles are similar if and only if the corresponding sides are in proportion and the corresponding angles are congruent. There are three ways to prove a triangle similar.

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Aim: Proving Triangles Similar

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  1. Aim: Proving Triangles Similar By: Michael Shi and Max Fiedziukiewicz

  2. Two triangles are similar if and only if the corresponding sides are in proportion and the corresponding angles are congruent. • There are three ways to prove a triangle similar.

  3. To show two triangles are similar, you must show that at least two angles on one triangle is congruent to two angles of another triangle. Theorem: If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.

  4. Theorem: If the three sets of corresponding sides of two triangles are in proportion, the triangles are similar.

  5. Theorem: If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar.

  6. 9 G A B 8 8 6 6 E F C 12 Are the Triangles similar?

  7. Can you find the value? 6 8 12 x

  8. Given- CB ll ED Prove- ∆acb similar ∆aed 1. 2. Given- DA bisector of angle CAB Prove- ∆CAD similar ∆ABD

  9. d x 3. Given- dxzg, abcd, and gfbe are squares, zf is congruent to zc Prove- ∆zaf ≈ ∆cge c e z g a b f

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