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 !