Download Geometric Proofs

Vocabulary
*Supplementary Angles: Two angles that add up to 1800.
*Complementary Angles: Two angles that add up to 900.
Linear Pair Theorem: If two angles forma linear pair, then they
are supplementary.
Angle Addition Postulate: If a point S lies in the interior of
∠PQR, then ∠PQS + ∠SQR = ∠PQR.
Vocabulary
Segment Addition Postulate: If a point B lies on a segment AC,
then AB + BC = AC.
B
A
C
Definition of Midpoint: A point on a line segment that divides it
into two equal parts (the halfway point of a line segment).
Definition of an Angle Bisector: A line that divides an angle into
two congruent angles.
Writing Justifications
Write a justification for
each step, given that A
and B are supplementary
and mA = 45°.
1. A and B are supplementary.
mA = 45°
Given information
2. mA + mB = 180°
Def. of supp s
3. 45° + mB = 180°
Subst. Prop of =
4. mB = 135°
Subtr. Prop of =
Example 1
Write a justification
for each step, given
that B is the midpoint
of AC and AB  EF.
1. B is the midpoint of AC.
Given information
2. AB  EF
Given information
3. AB  BC
Def. of mdpt.
4. BC  EF
Trans. Prop. of 
Writing a Two-Column Proof
Write a two-column proof.
Given: 1 and 2 are supplementary, and
1  3
Prove: 3 and 2 are supplementary.
Statements
Reasons
1. 1 and 2 are supplementary. 1. Given
1  3
2. m1 + m2 = 180°
of supp. s
2. Def.
.
= m3
3. m1
.
3. Def. of  s
4. m3 + m2 = 180°
4. Subst.
5. 3 and 2 are supplementary 5. Def. of supp. s
Write a two-column proof.
Given: 1 and 2 are complementary, and
2 and 3 are complementary.
Prove: 1  3
Statements
Reasons
1. 1 and 2 are complementary. 1. Given
2 and 3 are complementary.
2. m1 + m2 = 90°
m2 + m3 = 90°
of comp. s
2. Def.
.
+ m2 = m2 + m3 3. Subst.
3. m1
.
4. m2 = m2
4. Reflex. Prop. of =
5. m1 = m3
5. Subtr. Prop. of =
6. 1  3
6. Def. of  s