Download Proving Triangles Similar Notes

Proving Triangles Similar Notes
Theorem 7.1 Angle – Angle Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle, then the
triangles are similar.
If angle A = angle D and angle B = angle E, then ∆ ABC ˜ ∆DEF.
Side –Angle – Side Similarity Theorem
If an angle of one triangle is congruent to an angle of a second triangle, and the sides
including the two angles are proportional, then the triangles are similar.
Angle A = Angle D
𝐴𝐵/𝐷𝐸 = 𝐴𝐶/𝐷𝐹, Then ∆ ABC ˜ ∆ DEF
Side-Side-Side Similarity Theorem
If the corresponding sides of two triangles are proportional, then the triangles are similar.
Theorem: The altitude to the hypotenuse of a right triangle divides the triangle into two
triangles that are similar to the original triangle and to each other.
The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of
the segments of the hypotenuse.
CD = √AD . DB = square root of AD times DB