Proofs

Symmetric

if a=b, then b=a line AB is congruent to line BA

Congruent Complements Theorum

If two angles are complementary to the same angle, then they are congruent

Linear Pair Postulate

If two angles form a inear pair, then they are supplementary

Given: angle A & angle B are rt angles Prove: angle A =~ angle B

1.) Angle A and angle B are rt angles; Given 2.) Angle A= 90° Angle B= 90°; Def. Of Rt angles 3.) m of angle A= m of angle B; Transitive 4.) Angle A=~ Angle B

Given: angle 1 and angle 3 are vertical Prove: angle 1 is congruent to angle 3, angle 2 is congruent to angle 4

1.) angle 1 and angle 3 are vertical; given 2.) angle 1 and angle 2 are supple., angle 2 and angle 3 are supple.; linear pair post. 3.) angle 1 is congruent to angle 3; Congruent Supplement Theorum

Given: angle 1 is congruent to angle 3 Prove: angle 2 is congruent to angle 4

1.) angle 1 is congruent to angle 3; given 2.) angle 1 is congruent to angle 2, angle 3 is congruent to angle 4; vertical angles are congruent 3.) angle 1 is congruent to angle 1 and angle 4; substitution 4.) angle 2 is congruent to angle 4; Transitive

Given: angle 1 and angle 2 is complementary, angle 2 and angle 3 is complentary Prove: angle 1 is congruent to angle 3

1.) angle 1& angle 2 is comp. angle 2 & and angle 3 is comp.; given 2.) measure of angle 1+ measure of angle 2= 90, measure of angle 2+ measure of angle 3=90; Def. of comp. 3.) measure of angle 1+ measure of angle 2 = measure of angle 2+measure of angle 3; Transitive 4.) measure of angle 1= measure of angle 3; Subtraction prop. of equality 5.) measure of angle 1 is congruent to measure of angle 3; Def. of Congruence

Given: angle 1& angle 2 are supple., angle 2 and angle 3 are supple. Prove: angle 1 is congruent angle 3

1.) angle 1& angle 2 is supple. angle 2 & and angle 3 is supple.; given 2.) measure of angle 1+ measure of angle 2= 180, measure of angle 2+ measure of angle 3=180; Def. of Supple. 3.) measure of angle 1+ measure of angle 2 = measure of angle 2+measure of angle 3; Transitive 4.) measure of angle 1= measure of angle 3; Subtraction prop. of equality 5.) measure of angle 1 is congruent to measure of angle 3; Def. of Congruence

Given: line AB is perp. to line BC, line DC is perp. to line BC Prove: angle B =~ angle C

1.) line AB is perp. to line BC, line DC is perp. to line BC; given 2.) angle B and angle C are rt. angles; def. of perp. 3.) angle B is congruent to angle C; rt angle theorum

Properties of Equality

Addition Subtraction Multiplication Division Distributive 2(x+3)=(x+3)+(x+3) Associative (Always Stays The Same) a+(b+c)=(a+b)+c Commutative (Change Order) a+b=b+a

Right Angle Congruence Theorum

All right angle are congruent

Congruent Supplements Theorum

If 2 angles are supplementary to the same angle, then they are congruent

Angle Addition Postulate

If point P is in the interior of angle RST, then the measure of angle RST=measure of angle RSP+ measure of angle PST

Congruence of Segments and Angles

Segments and Angles congruence is reflexive, symmetric, and transitive

Vertical angles Congruence Theorum

Vertical angles are congruent

Reflexive

a=a or angle A is congruent to angle A

Transitive

a=b, b=c, then a=c or angle A is congruent to angle B, angle B is congruent to angle C, then angle A is congruent to angle C

Linear Pair

two adjacent angles that form a line *(adjacent and supplementary)

Adjacent angles

two angles who share a common vertex and a common side

Supplementary angles

two angles whose angles equal 180 degrees

Vertical Angles

two angles whose sides form opposite rays