October 1st

In section 2.8, we learned many things dealing with angles. We learned how to prove angle relationships using protractors, we learned angle addition postulates, complements and supplements, properties of angle congrunce, and angle theorems.



Proving angle relationships:
Protractor Postulate- Given segment AB and a number "r" between zero and one eighty is exactly one ray, with endpoint "A" such that the measure of angle is "r"




Angle Addition Postulate:
If point "S" is in the interior of angle PAT then.. measure of angle PAS + measure of angle TAS = measure of angle PAT

measure of angle PAS and measure of angle TAS are adjacent angles... they share a vertex and one side and no other points.. this is just like segment addition postulate.

Complemens and Supllements:
Supplement Theorem- if two angles form a linear pair, then they are supplementary
Complement Theorem- if the noncommon sides of 2 adjacent angles form a right angle, then the 2 angles are complementary

Properties of Angle Congruence:
Angle congruence-
reflexive= for any angle ABC, angle ABC is congruence to angle to ABC
Symmetric= if angle ABC is congruent to angle DE, then angle is DEF is
congruent to angle ABC.
Transitive= if angle ABC is congruent to angle DEF and angle DEF is
congruent to angle GHI then angle ABC is congruent to angle GHI

Angle Theorems:
Congruent Supplements Theorem
If two angles are supplementary to the same angle (or to the congruent angles) then they are congruent
Example: if the measure of angle 1 + measure of angle 2 and measure of angle 3 + measure of angle two = 180 degrees, then angle 1 is congruent to angle 3
COngruent Complements Theorem
if two angles are complementary to the same angle (or to congruent angles) then they are congruent.
Example: if measure of angle 4 + measure of angle 5 = 90 degrees and measure of angle 5 + measure of angle 6 = 90 degrees.. then measure of angle 4 is congruent to measure of angle 6.

More Angle Theorems
perpendicular lines intersect to form right angles
all right angles are congruent
perpendicular lines form congruent adjacent angles
if two angles are both congruent and supplementary then each is a right angle
if two congruent angles form a linear pair, then they are right angles.

Last Angle Theorem:
Verticle angles Theorem- verticle angles are congruent