Chapter 4-Triangles Flashcards
triangle sum conjecture
the sum of the measures of the angles in every triangle is 180 degrees
auxillary line
an extra line or segment that helps with a proof
third angle conjecture
if two angles of one triangle are equal in measure to two angles of another triangle, then the third angles in each triangle are equal to each other
isosceles triangle conjecture
if a triangle is isosceles, then the base angles are congruent
equilateral triangle
a triangle with three congruent sides, a special type of isosceles triangle
triangle inequality conjecture
the sum of the lengths of any two sides of a triangle is greater than the length of the third side
side-angle inequality conjecture
in a triangle, if one side is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side
exterior angle
angle on the outside of the triangle, created by extending one side of a triangle beyond its vertex
adjacent interior angle
angle next to the exterior angle that lies on the inside of the triangle
remote interior angles
angles away from the exterior angle that lie on the inside of the triangle
exterior angles of a triangle conjecture
the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles
converse of the isosceles triangle conjecture
if a triangle has two congruent angles, then the base angles are congruent
System of equations
A set of two or more equations with the same variables
Solution to a system of equations
The point(s) that make all of the equations in the system true
Intersection point
The solution to a system on a graph
Substitution
Isolate one of the variables, then replace in the other equation
Elimination
Multiply one equation so one variable cancels with the other equation
Congruent
Having the same size and shape
Included angle
An angle that is included between two sides of a triangle
Included side
A side that is included between two angles of a triangle
SSS congruence
If three sides of one triangle are congruent to three sides of another triangle then the triangles are congruent
SAS congruence conjecture
If two sides and the included angle of one triangle are congruent to two sides and the included angle if another triangle then the triangles are congruent
ASA congruence conjecture
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle then the triangles are congruent
SAA congruence conjecture
If two angles and a non included side of one triangle are congruent to the two corresponding angles and the non included side of another triangle the the triangles are congruent
Valid congruence shortcuts
SSS
SAS
ASA
SAA
Invalid congruence shortcuts
AAA
ASS
CPCTC
Corresponding Parts of Congruent Triangles are Congruent
Vertex angle bisector conjecture
In an isosceles triangle, the bisector of the vertex angle is also the median and altitude to the base
