Similarity & Congruency Dr. Marinas

Similarity Has same shape All corresponding pairs of angles are congruent Corresponding pairs of sides are in proportion

Similarity Example Angle A  Angle D Angle B  Angle E Angle C  Angle F AB = BC = AC DE EF DF  ABC   DEF

Proving Similarity (AAA) - Angle, Angle, Angle If three angles of one triangle are congruent, respectively, to three angles of a second triangle, then the triangles are similar. AAA AA

Congruency Has same shape and same size All corresponding pairs of angles are congruent Corresponding pairs of sides are congruent.

Congruency Example Angles  Angle A  Angle D Angle B  Angle E Angle C  Angle F Sides  AB  DE BC  EF CA  FD

Side, Side, Side (SSS) If the three sides of one triangle are congruent, respectively, to the three sides of a second triangle, then the triangles are congruent.

Side, Angle, Side (SAS) If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, respectively, then the two triangles are congruent.

Angle, Side, Angle (ASA) If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, respectively, then the two triangles are congruent.

Angle, Angle, Side (AAS) If two angles and a corresponding side of one triangle are congruent to two angles and a corresponding side of another triangle, respectively, then the two triangles are congruent.

Congratulations! You are now a similarity and congruency expert !