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