Chapter 4-Triangles

Question 1

triangle sum conjecture

Answer 1

the sum of the measures of the angles in every triangle is 180 degrees

Question 2

auxillary line

Answer 2

an extra line or segment that helps with a proof

Question 3

third angle conjecture

Answer 3

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

Question 4

isosceles triangle conjecture

Answer 4

if a triangle is isosceles, then the base angles are congruent

Question 5

equilateral triangle

Answer 5

a triangle with three congruent sides, a special type of isosceles triangle

Question 6

triangle inequality conjecture

Answer 6

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

Question 7

side-angle inequality conjecture

Answer 7

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

Question 8

exterior angle

Answer 8

angle on the outside of the triangle, created by extending one side of a triangle beyond its vertex

Question 9

adjacent interior angle

Answer 9

angle next to the exterior angle that lies on the inside of the triangle

Question 10

remote interior angles

Answer 10

angles away from the exterior angle that lie on the inside of the triangle

Question 11

exterior angles of a triangle conjecture

Answer 11

the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles

Question 12

converse of the isosceles triangle conjecture

Answer 12

if a triangle has two congruent angles, then the base angles are congruent

Question 13

System of equations

Answer 13

A set of two or more equations with the same variables

Question 14

Solution to a system of equations

Answer 14

The point(s) that make all of the equations in the system true

Question 15

Intersection point

Answer 15

The solution to a system on a graph

Question 16

Substitution

Answer 16

Isolate one of the variables, then replace in the other equation

Question 17

Elimination

Answer 17

Multiply one equation so one variable cancels with the other equation

Question 18

Congruent

Answer 18

Having the same size and shape

Question 19

Included angle

Answer 19

An angle that is included between two sides of a triangle

Question 20

Included side

Answer 20

A side that is included between two angles of a triangle

Question 21

SSS congruence

Answer 21

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

Question 22

SAS congruence conjecture

Answer 22

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

Question 23

ASA congruence conjecture

Answer 23

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

Question 24

SAA congruence conjecture

Answer 24

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

Question 25

Valid congruence shortcuts

Answer 25

SSS
SAS
ASA
SAA

Question 26

Invalid congruence shortcuts

Answer 26

AAA

ASS

Question 27

CPCTC

Answer 27

Corresponding Parts of Congruent Triangles are Congruent

Question 28

Vertex angle bisector conjecture

Answer 28

In an isosceles triangle, the bisector of the vertex angle is also the median and altitude to the base