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.
