Geometry Triangles

triangle

A 3 sided polygon.

polygon

A closed figure formed by three or more line segments

acute triangle

A triangle with 3 acute angles

right triangle

a triangle with 1 right angle

obtuse triangle

A triangle with 1 obtuse angle

equiangular triangle

A triangle with 3 congruent angles each measure 60 degrees

scalene triangle

A triangle with no congruent sides.

isosceles triangle

A triangle with at least 2 congruent sides

equilateral tringle

A triangle with 3 congruent sides

Interior Angle Sum Thm

The sum of the interior angles of a triangle is 180 degrees

Exterior Angle Thm

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

Isosceles Triangle Thm

The base angles of an isosceles triangle are congruent

congruent triangles

2 triangles are congruent if and only if all pairs of corresponding sides and angles are congruent

SSS

If 3 sides of one triangle are congruent to 3 sides of another triangle, then the triangles are congruent

SAS

If 2 sides and an included angle of a triangle are congruent to 2 sides and included angle of aother triangle, then the triangles are congruent

ASA

If 2 angles and an included side of a triangle are congruent to 2 angles and included side of another triangle, then the triangles are congruent

AAS

If 2 angles and a non-included side of one triangle are congruent to 2 angles and a non-included side of another triangle, then the triangles are congruent

HL

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.

CPCTC

If two triangles are congruent, then their corresponding parts are congruent.

median of a triangle

A segment from a vertex to the midpoint of the opposite side.

altitude of a triangle

The perpendicular segment form a vertex to the line containing the opposite side.

Similar Triangles

Two triangles with corresponding angles equal and corresponding sides proportional