Properties, Postulates, Definitions, Theorems, and Proofs

Definition of supplementary

m<1+m<2=180 <1 supplementary <2

Definition of right angle

m<1=90 <1 is a right <

Definition of angle bisector

ray QR bisects <PQS <PQR≅<RQS

Definition of segment bisector

segment BE bisects segment CF at E GIVEN segment CE≅segment EF

Complement theorem

If the non-common sides of two adjacent angles form a right angle, then the angles are complementary.

Vertical angles theorem

If two angles are vertical angles, then they are congruent.

Definition of complementary

<1 complementary <2 m<1+m<2=90

Transitive

<1≅<2 <2≅<3 <1≅<3

Definition of congruence

<1≅<2 m<1=m<2

Definition of right angle

<8 is a right angle. segment BC ⊥ segment BA

Definition of right angle

<ABC is a right angle. m<ABC=90

Congruent complements theorem

Angles complementary to congruent angles are complementary.

Congruent complements theorem

Angles complementary to the same angle are complementary.

Congruent supplements theorem

Angles supplementary to congruent angles are congruent.

Congruent supplements theorem

Angles supplementary to the same angle are congruent.

SAP

DC+CB=DB

Multiplication

If AB=CD, then 3 AB=3 CD.

Symmetric

If AB=CD, then CD=AB.

Definition of midpoint

If X is the midpoint of AB, then AX=XB.

Supplement theorem

If angles form a linear pair, then they are supplementary angles.

Subtraction

If m<1+m<2=m<2+m<3, then m<1=m<3.

Supplementary theorem

If m<4 and m<9 form a linear pair, then <4 supplementary <9.

Definition of perpendicular lines

Perpendicular lines intersect to form four right angles.

Right angle theorem

˙All right angles are congruent. ˙Perpendicular lines form congruent adjacent angles. ˙If two angles are congruent and supplementary, then each angle is a right angle. ˙If two congruent angles form a linear pair, then they are right angles.