Math Things

 $m\angle ABD+m\angle DBC=m\angle ABC$  

• Angle addition postulate

• Vertical angles Theorem

• Def. of a right angle

• Complement theorem

If two angles are vertical, then they are congruent.

• Def. of perpendicular

• Complement theorem

• Vertical angles theorem

• Def. of a right angle

 $m\angle A=m\angle B\leftrightarrow\angle A\cong\angle B$  

• Def. of perpendicular

• Complement theorem

• Def. of congruence

• Def. of a right angle

A right angle $=$  90 $\degree$  

• Def. of a right angle

• Def. of congruence

• Def. of perpendicular

• Complement theorem

Perpendicular lines form right angles.

• Supplement theorem

• Congruent Complements theorem

• Def. of supplementary angle

• Def. of perpendicular

Supplementary $\leftrightarrow$  sum is 90 $\degree$  

• Supplement theorem

• Def. of supplementary angles

• Complement theorem

• Def. of angle bisector

An angle bisector divides and angle into two equal parts.

• Def. of angle bisector

• Def. of complementary angles

• Complement theorem

• Supplement theorem

Complementary $\leftrightarrow$  sum is 90 $\degree$  

• Def. of complementary angles

• Complement theorem

• Supplement theorem

• Congruent supplements theorem

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

• Def. of angle bisector

• Def. of perpendicular

• Supplements theorem

• congruent complements theorem

If two angles form a right angle, then they are complementary

• Complement theorem

• Angle addition postulate

• Congruent Complements theorem

• Congruent supplements theorem