Angles & Proofs

angle measure

formed by 2 rays with a common endpoint

name a angle with 3 letters

radians

name the angle with the vertex in the middle

degrees

results from dividing the distance around a circle into 360 parts

a protractor can be used to measure angles

angle addition postulate

angle AOB+ angle BOP= angle AOP

classifying angles

acute angle

measure of angle <90 degrees

right angle

measure of angle = 90 degrees

obtuse angle

measure of angle >90 degrees

straight angles

measure of angle = 180 degrees

angle bisectors

a ray that divides an angle into two congruent angles

angle pair relationships

intersecting lines

2 lines that meet at exactly 1 point

parallel lines

2 lines that NEVER intersect (same slope but different y-intersect)

perpendicular lines

intersect to form 4 right angles

intersect to form congruent adjacent angles

segments and rays can be perpendicular to lines or other line segments and ray

right angle symbols indicates that the lines are perpendicular

adjacent angles

2 angles that share a common vertex and side

complementary angles

2 angles with measures that have a sum of 90 degrees

2 angles doesn't have to be adjacent

congruent complements theorom

if 2 angles are complement to the same angles or to congruent angles, then the 2 angles are congruent

supplementary angles

2 angles with measures that have a sum of 180 degrees

congruent supplements theoroms

if 2 angles are supplementary or to the same angle or congruent angles, then the 2 angles are congruent


special angle pairs

vertical angles

linear pair

a pair of adjacent angle formed when 2 line intersect.

always are supplementary, which means their measures add up to 180 degree

linear pair postulate

2 nonadjacent angles formed by 2 intersecting lines

vertical angles are always congruents

assume

you can assume relationships that depends on placements

you cannot assume relationship that depends on measures

proofs

definition of segment bisector

if segment AC bisects segment BD, then E is the midpoint of segment BD

definition of perpendicular lines

If segment AB perpendicular to segment BC, then angle ABC is a right angle

def. of supplementary angles

If measure of angle 6+measure of angle7=180 degrees, then angle 6 is a supplement of angle 7

def. angle bisector

If segment CE bisects angle DCB, then measure of angle 3=measure of angle4

vertical angle congruent theorom

addition property

measure of angle 5=measure of angle 7, they are vertical angles

def. of complementary angles

If angle 1 and angle 2 are complementary, then angle1+angle2=90 degrees

If measure of angle 1= measure of angle 4 and measure of angle 2=measure of angle 3, the measure of angle1+measure of angle 2=measure angle 3+ measure of angle4

def. right ∠'s

If angle DCB=90 degrees, the angle DCB is a right angle.

congruent supplement theorom

If angle5 is supplementary to angle 6 and angle 6 is supplementary to angle 7, then measure of angle 5= measure of angle 7

angle addition postulate

measure of angle 1=measure of angle 2=measure of angle ABC

transitive property

If measure of angle 8=measure of angle 1 and measure of angle 1 = measure of angle 9, then measure of angle 8 =measure of angle 9

def. of midpoint

If E is the midpoint of segment AC, then AE=EC

substitution property

If measure of angle1+meaasure of angle2=90 degrees and measure of angle 2=45 degrees, then measure of angle 1+45degrees=90degrees

symmetric property

If measure of angle1=measure of angle4, then measure of angle4=measure of angle1

subtraction property

If measure of angle ABC= measure of angle DCB and measure of angle1 = measure of angle 4, then measure of angle ABC- measure of angle1= measure of angle DCB- measure of angle 4

reflexive property

measure of angle3= measure of angle 3

congruent complement theorom

If measure of angle1 is complementary to angle 2 and angle 3 is complementary to angle 4 and measure of angle 1 = measure of angle 4, then measure of angle 2 = measure of angle 3

diagrams of proofs

2 columnes

flowchart

paragraph