LESSON 3 (TRIANGLE CONGRUENCE POSTULATES AND THEOREMS)

Figures that have exact same size and shape

Congruent figures

All six corresponding parts of the two triangles are equal: three sides and three angles

Congruent triangles

One of the most common figures used to study congruence

Triangle

Are equal in both sides and shape, which means that all corresponding sides have the same length and all corresponding angles have the same measure

Congruent triangles

Have equal corresponding angles, but their corresponding sides are only proportional and not necessary equal in length

Similar triangles

Properties of congruence

• Reflexive Property of Congruence

• Symmetric Property of Congruence

• Transitive Property of Congruence

Any figure is congruent to itself

Reflexive Property of Congruence

If one figure is congruent to another, then the second figure is congruent to the first

Symmetric Property of Congruence

If one figure is congruent to a second figure, and the second is congruent to a third, then the first is congruent to the third

Transitive Property of Congruence

Postulates and theorems involving congruent triangles

• Third Angle Theorem

• The SSS Congruence Postulate (Side-Side-Side)

• The SAS Congruence Postulate (Side-Angle-Side

• The ASA Congruence Postulate (Angle-Side-Angle)

• The AAS Congruence Theorem (Angle-Side-Angle)

Is an angle formed between two given sides of a triangle

Included Angle

Is a side found between two given angles of a triangle

Included side

If two angles of one triangle are congruent to two angles of another triangle, then the third angle is also congruent to the third angle of another triangle

Third Angle Theorem

If three sides of one triangle are congruent to the corresponding three sides of another triangle, then the two triangles are congruent

The SSS Congruence Postulate (Side-Side-Side)

If two sides and the included angle of one triangle are congruent to the corresponding two sides and the included angle of another triangle, then the two triangles are congruent

The SAS Congruence Postulate (Side-Angle-Side)

If two angles and the included side of one triangle are congruent to the corresponding two angles and the included side of another triangle, then the triangle are congruent

The ASA Congruence Postulate (Angle-Side-Angle)

If two angles and non-included side of one triangle are congruent to the corresponding two angles and a non-included side of another triangle, then the two triangles are congruent

The AAS Congruence Theorem (Angle-Angle-Side)