Unit 4 Congruent Triangles vocabulary

Scalene

No congruent sides

Isosceles Triangle

A triangle with at least 2 congruent sides

Acute triangle

3 acute angles

Obtuse triangle

1 obtuse angle

Equiangular

3 congruent angles

Triangle Sum Theorem

The measure of the angles of a triangle adds up to 180 degrees.

Exterior angles

Make a linear pair with an interior angle

Exterior Angle Theorem

The measure of an exterior angle is equal to the sum of the 2 non-adjacent interior angles.

Corollary to the Triangle Sum Theorem

In a right triangle, the acute angles are complementary.

Congruent triangles

2 triangles are congruent if they have 3 pairs of congruent sides and 3 pairs of congruent angles.

Third Angles Theorem

If 2 angles of one triangle are congruent to 2 angles in another triangle, then the 3rd pair of angles are congruent.

Properties of congruent triangles:

Reflexive POCT

Symmetric POCT

Transitive POCT

Side-Side-Side Congruence Postulate (SSS Congruence)

If 3 sides of one triangle are congruent to 3 sides of another triangle, then the 2 triangles are congruent to each other.

Included angle

The angle made by two sides of a triangle.

Side-Angle-Side Congruence Postulate (SAS Congruence)

If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

Side-Side-Angle Sometimes Congruence Theorem (SSA sometimes)

If two sides of a triangle are congruent to two sides of another triangle, and a non-included angle of the first is congruent to the corresponding non-included angle of the second, then the triangles are congruent when the angles are right.

Angle-Side-Angle Congruence Postulate (ASA Congruence)

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

Angle-Angle-Side Congruence Theorem (AAS Congruence)

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

Base Angles Theorem

In a triangle, if two sides are congruent, then the angles opposite those sides are congruent.

Base Angles Converse

In a triangle, if two angles are congruent, then the opposite sides are congruent.

Isosceles Triangle Rule

In an isosceles triangle, if you draw a perpendicular line or an angle bisector or a segment bisector from the vertex, you’ve drawn all 3 of them.

Equilateral Triangle Theorem

A triangle is equilateral if and only if it is equiangular.