Geometry Chapter 4 Test

The triangle sum theorem

the sum of the measures of the interior angles in a triangle is 180 degrees

exterior angle theorem

the measure of the exteriot angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of a triangle

right trianlgle (angle)

has one right angle

acute triangle (angles)

has all acute angles

obtuse triangle (angles)

has one obtuse angle

equilangular triangle (angles)

has all congruent angles (60 degrees each)

equilateral triangle (sides)

has three congruent sides

isoceles triangle (sides)

has at least two congruent sides

scalene triangle (sides)

no congruent sides

def of congruent shapes

if you can move, turn, or flip one shape so that it perfectly overlaps the other, the shapes are congruent. These are called RIGID transformations. (all corresponding parts with be congruent)

the third angles theorem

if two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent

SSS (side-side-side)

if three sides of one triangle are congruent to three sides of a second triangle, then the trianlges are congruent

SAS (side-angle-side)

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 triangles are congruent

included angle

angle that connects the two known congruent sides

ASA (angle-side-angle)

if two angles and the included side of one triangle are congruent to two angles and the included side of another trianggle, then the triangles are congruent

included side

side that connects the two known congruent angles

AAS (angle-angle-side)

if two angles and the non-included side of one triangle are congruent to two angles and the non-included side of a second triangle then the triangles are congruent

when does SSA work

SSA doesn’t guarantee congruence EXCEPT in the case where the triangles are right triangle

HL (hypotenuse-leg)

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

CPCTC (corresponding parts of congruent triangles are congruent)

if there are congruent triangles, then the corresponding parts of triangles are congruent

process of CPCTC

1. use what is given to show triangles congruent

2. write a triangle congruence statment

3. use CPCTC to state all other corresponding angles and/or sides are congruent too

parts of isoceles triangles: the two congruent sides are called ?

parts of isoceles triangles: the two congruent sides are called the legs

parts of isoceles triangles: the angle where the legs intersect is ?

parts of isoceles triangles: the angle where the legs intersect is called the vertex angle

parts of isoceles triangles: the side opposite the vertex is called?

parts of isoceles triangles: the side opposite the vertex is called the base

parts of isoceles triangles: the angles along the base are called ?

parts of isoceles triangles: the angles along the base are called the base angles

isosceles triangle theorem

if two sides of a triangle are congruent, then the angles opposite those sides are congruent

converse of isosceles triangle theorem

if two angles of a triangle are congruent, then the sides opposite those angles are congruent

equilateral triangles: if a triangle is equilateral, then the triangles is ?

equilateral triangles: if a triangle is equilateral, then the triangles is equilangular

equilateral triangles: if the sides are congruent, then the angles must be ?

equilateral triangles: if the sides are congruent, then the angles must be congruent to each other

equilateral triangles: if a triangle is equilangular, then the triangles is ?

equilateral triangles: if a triangle is equilangular, then the triangles is equilateral

equilateral triangles: if 3 angles of a triangle are congruent (all 60 degrees), then the 3 sides must be?

equilateral triangles: if 3 angles of a triangle are congruent (all 60 degrees) then the 3 sides must be congruent to each other

which triangle combos don't work to prove congruence

SSA and AAA