Triangles

angle side angle post

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

side side side congruence post

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

side angle side congruence post

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

angle angle side thm

If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles arecongruent.

AA~

if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar

SAS~

If an angle of one triangle is congruent to an angle of a second triangle, and the side that includes the two angles are proportional, then the triangles are similar

SSS~

If the corresponding sides of two triangles are proportional, then the triangles are similar

equilateral

All SIDES are congruent

equiangular

All ANGLES are congruent

isosceles

Two congruent sides

scalene

No congruent sides

vertex

Each of the three points joining the side

adjacent sides

Two sides sharing a common vertex

third angle thm

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

angle bisector

Aplits the angle in half

incenter

The point of congruency for angle bisector’s

perpendicualr bisector

A segment to a side of a triangle at the end point of that side

circumcenter

The point of congruency for perpendicular bisector’s

altitude

A segment from a vertex to the opposite side and is perpendicular to that side

othercenter

The point of congruency for altitude’s

median

A segment whose endpoints are a vertex and the midpoint of the vertex of the opposite side

centroid

The point of congruency for median’s

indirect proof

Always start with we assume

indirect proof

Right out the proof as if you were trying to prove the opposite then contradicting yourself to prove your point

comparison property of equality

if a+b=c and c>0, then a>b

Corollary to the triangle exterior angle thm

the measure of an exterior angle of a triangle is greater than the measure of each of its remote angles

triangle inequality thm

the sum of two sides of a triangle is greater than the length of the third side

hinge thm

If two sides of a triangle are congruent to two sides of another triangle, but the angle of those sides aren’t congruent, then how long the third side is will be determined by how big the angle is

converse of the hinge thm

If two sides of a triangle are congruent to two sides of another triangle then, then the length of the angle will determine how big the side is