1. POSTULATES AND THEOREMS USED IN PROVING:
LECTURE NO. 1
Properties of Equalities:
1. Reflexive Property of Equality (RPE)
x = x, for every real number x.
Example:
STATEMENTS REASONS
1. AB AB 1. Reflexive Property of Equality
2. Symmetric Property of Equality (SymPE)
For any real numbers x and y, if x = y, then y = x.
Example:
STATEMENTS REASONS
1. m ABC = m DEF 1. Definition of Congruent Angles
2. m DEF = m ABC 2. Symmetric Property of Equality
3. Transitive Property of Equality (TPE)
For any real numbers x , y and z, if x = y, and y = z, then x = z.
Example:
STATEMENTS REASONS
1. m ABC = m DEF 1. Definition of Congruent Angles
2. m DEF = m XYZ 2. Definition of Congruent Angles
3. m ABC = m XYZ 3. Transitive Property of Equality
Geometric Terms:
1. Angle Bisector
The angle bisector divides the angle into two congruent angles.
B
A C
D

2. Example:
STATEMENTS REASONS
1. BD is the angle bisector of ABC. 1. Given
2. ABD CBD 2. Definition of Angle Bisector
2. Midpoint
The midpoint divides the line segment into two congruent line segments.
Example:
STATEMENTS REASONS
1. D is the midpoint of AC. 1. Given
2. 2. Definition of Midpoint
Pairs of Angles:
1. Complementary Angles
Angles are complementary if the sum of their measures is 90 o.
Example:
STATEMENTS REASONS
1. m ABC + m DEF = 90 1. Definition of Complementary Angles
2. Supplementary Angles
Angles are complementary if the sum of their measures is 180 o.
Example:
STATEMENTS REASONS
1. m ABC + m DEF =180 1. Definition of Supplementary Angles
3. Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.
Example:
STATEMENTS REASONS
1. 1 and 2 form a linear pair. 1. Given
2. 1 and 2 are supplementary. 2. Linear Pair Postulate

3. 4. Vertical Angle Theorem (VAT)
Vertical Angles are congruent.
3 4
Example:
STATEMENTS REASONS
1. 3 4 1. Vertical Angle Theorem (VAT)
5. Perpendicular Lines
Perpendicular lines form right angles.
K Q
L R
J P
Example:
STATEMENTS REASONS
1. KJ KL and QP QR 1. Given
2. K and Q are right angles 2. Definition of Perpendiculars
6. Any two right angles are congruent.
Example:
STATEMENTS REASONS
1. KJ KL and QP QR 1. Given
2. K and Q are right angles 2. Definition of Perpendiculars
3. K Q 3. Any two right angles are congruent