Geometry 6.3 & 6.4 Prove Triangles are Similar by AA, SAS, SSS

7.

8.

10.

9.

11.

 Cut this and place it on the left hand-side of your INB.                                    

 

SIDE-SIDE-SIDE (SSS) SIMLARITY POSTULATE: If the corresponding side lengths of two triangles are proportional then the triangles are similar.

If ,

then ΔABC ~ ΔRST.

SIDE-ANGLE-SIDE (SAS) SIMLARITY POSTULATE: If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are ___________________, then the triangles are similar.

If ∠X ≅ ∠M and

, then ΔXYZ ∼

ΔMNP.

Triangle Similarity Postulate and Theorems:

AA Similarity Postulate: If ∠A ≅ ∠D and ∠B ≅ ∠E, then ΔABC ~ ΔDEF. (If 2 angles of 1 triangle = 2 angles of another triangle they are similar)

SSS Similarity Theorem: If , then ΔABC ~ ΔDEF.

(If all sides of 1 triangle are proportional to all sides of another triangle they are similar)

SAS Similarity Theorem: If ∠A ≅ ∠D and , then ΔABC ∼ ΔDEF.

(If all 2sides of 1 triangle proportional to 2 sides of another triangle and the included angles are = then the triangles are similar

ANGLE –ANGLE (AA) SIMLARITY POSTULATE: ∆JKL ~ ∆XYZ If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.