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