Question

Two triangles are congruent if and only if their corresponding parts are congruent.

a. What is the AAS postulate?
b. What is the ASA postulate?
c. What is the CPCTC?
d. What is the SAS postulate?

Answer 1

The AAS postulate states that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. The ASA postulate states that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent. The CPCTC refers to the statement that corresponding parts of congruent triangles are congruent. The SAS postulate states that if two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Step-by-step explanation:

The AAS postulate states that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. For example, if angle A is congruent to angle D, angle B is congruent to angle E, and side AB is congruent to side DE, then triangle ABC is congruent to triangle DEF.

The ASA postulate states that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. For example, if angle A is congruent to angle D, angle B is congruent to angle E, and side AB is congruent to side DE, then triangle ABC is congruent to triangle DEF.

The CPCTC or Corresponding Parts of Congruent Triangles are Congruent is a statement used to conclude that corresponding parts of congruent triangles are congruent. This is used as a reason in proving congruence of triangles. For example, if triangle ABC is congruent to triangle DEF, then we can conclude that angle A is congruent to angle D, side AB is congruent to side DE, and so on.

The SAS postulate states that if two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. For example, if side AB is congruent to side DE, side BC is congruent to side EF, and angle B is congruent to angle E, then triangle ABC is congruent to triangle DEF.