Geometry Chapter 4 Theorems, Postulates, Definitions

Front 1

Acute Triangle

Back 1

All angles are acute. (Less than 90 degrees.)

Front 2

Obtuse Triangle

Back 2

One angle is obtuse. (Greater than 90 degrees.)

Front 3

Right Triangle

Back 3

One angle is right. (Equals 90 degrees.)

Front 4

Scalene Triangle

Back 4

No two sides of a triangle are congruent.

Front 5

Isosceles Triangle

Back 5

At least two sides of a triangle are congruent.

Front 6

Equilateral Triangle

Back 6

All sides of a triangle are congruent.

Front 7

Angle Sum Theorem

Back 7

The sum of the measures of the angles of a triangle is 180 degrees.

Front 8

Third Angle Theorem

Back 8

If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.

Front 9

Exterior Angle Theorem

Back 9

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

Front 10

Definition of Congruent Triangles

(CPCTC)

Back 10

Two triangles are congruent iff (if and only if) their corresponding parts are congruent.

(Corresponding Parts of Congruent Triangles are Congruent - CPCTC)

Front 11

Congruence of Triangles is:

Back 11

Reflexive,
Symmetric and
Transitive

Front 12

SSS Postulate
(Side-Side-Side)

Back 12

If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.

Front 13

ASA Postulate
(Angle-Side-Angle)

Back 13

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

Front 14

AAS Postulate
(Angle-Angle-Side)

Back 14

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

Front 15

Isosceles Triangle Theorem

Back 15

If two sides of a triangle are congruent, the the angles opposite those sides are congruent.

Front 16

Converse of the Isosceles Triangle Theorem

Back 16

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.