Similarity and Congruent Triangles

Similarity and Congruent Triangles

Mrs. Cagle's Math 2 Class

Similar and Congruent Postulates

• Postulate: A statement, also known as an axiom, which is taken to be true without proof.

• Theorem: a general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths

SAS=Side Angle Side Postulate

• SAS: states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

ASA: Angle Side Angle Postulate

• ASA: states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

AAS: Angle Angle Side Postulate

• AAS: states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

SSS: Side Side Side

• SSS: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. Congruence of sides is shown with little hatch marks, like this: ∥. For two triangles, sides may be marked with one, two, and three hatch marks.

HL: Hypotenuse Leg Postulate

• HL: The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

CPCTC: Corresponding Parts of Congruent Triangles are Congurent

• CPCTC: is an acronym for corresponding parts of congruent triangles are congruent.

Writing a Proof

Statements/Reasons 

Multiple Choice

How are triangle ABC and triangle A'B'C' Congruent?

• SAS

• AAS

• ASA

• HL

Multiple Choice

How would you prove triangle MPN and triangle RSQ are congruent?

• ASA

• SSS

• SAS

• CPCTC

Multiple Choice

How would prove triangle ABC and triangle DEF are congruent?

• SSS

• AAS

• HL

• CPCTC