Download Proving Similar Triangles Review Sheet

Proving Similar Triangles Review Sheet You can always prove that two triangles are similar by showing that they satisfy the two requirements for similar polygons. 1.) Show that corresponding angles are congruent AND 2.) Show that corresponding sides are proportional. However, there are 3 simpler methods. Angle-­‐Angle Similarity Postulate ( AA~ ) If two angles of one triangle are congruent to two angles of another triangle then the triangles are similar. Examples of AA~ The ΔABC ~ ΔXZY are similar by AA~ because 1) They are both right triangles; therefore they both have a 90 degree angle. 2) All triangles add up to 180 degrees, since angle C is 40 degrees in ΔABC angle A will be 50 degrees. Therefore, ∠ A and ∠ X are congruent. The ΔGHJ ~ ΔGMK are similar by AA~ because 1) ∠ H and ∠ M are congruent by Corresponding Angles Postulate. 2) ∠ G and ∠ G are congruent since they are the same angle. Side-­‐Side-­‐Side Similarity (SSS~): If the three sides of one triangle are proportional to the three sides of another triangle, then the two triangles are similar. Example of SSS~ ΔFHG ~ ΔXRS because three sides of one triangle are proportional to three sides of another triangle. 𝐹𝐻 10 5
=
= 𝑋𝑅 16 8
𝐻𝐺 15 5
=
= 𝑅𝑆 24 8
𝐹𝐺 20 5
=
= 𝑋𝑆 32 8
Side-­‐Angle-­‐Side Similarity (SAS~): If two sides of one triangle are proportional to two sides of another triangle and the included angles of these sides are congruent, then the two triangles are similar. Example of SAS~ ΔRSQ ~ ΔUST because 1) ∠ S ≅ ∠ S since Vertical Angles are Congruent 2)
!"
!"
!"
!"
=
=
!"
!
!
!
!
= , Two sides of one triangle are proportional to two sides of another triangle. !
!
= !