Download Parallel Line Proof Puzzle #1

Linear Pair Theorem Puzzle Proof
If two angles form a linear pair,
Then the angles are supplementary.
Given: 1 and 2 form a linear pair.
Prove:
1 2
1 and 2 are supplementary.
Statements
T
A
M
Reasons
1 and 2 form a linear pair
Given
TAM is a straight angle.
Definition of Linear Pair
Two angles form a linear pair
iff their non-shared sides form a straight angle..
Definition of straight angle
m TAM = 180
An angle is a straight angle,
iff its measure is 180 .
Angle Addition Postulate
If two angles are adjacent,
then the sum of their individual measures equals the
measure of the angle formed by their non-shared
sides.
m1 + m 2 = mTAM
Substitution Property of Equality
m1 + m 2 = 180
If m 1 + m  2 = m TAM and mTAM = 180
Then m1 + m 2 = 180
Definition of Supplementary
1 and 2 are supplementary
The measure of two angles sums to 180
iff the angles are supplementary.
QED
Vertical Angles Theorem Puzzle Proof
If two angles are vertical angles,
Then they have equal measures.
Given: 1 and 2 are vertical angles
2
1 3
Prove: m1 = m 2
Statements
Reasons
1 and 2 are vertical angles
Given
1 and 3 form a linear pair
2 and 3 form a linear pair
Definition of Linear Pair
1 and 3 are supplementary
2 and 3 are supplementary
Linear Pair Theorem
Two angles form a linear pair
iff their non-shared sides form a straight angle.
If two angles form a linear pair,
then they are supplementary.
m1 + m 3 = 180
m 2 + m  3 = 180
Definition of Supplementary
The measure of two angles sums to 180
iff the angles are supplementary.
Subtraction Property of
Equality
m1 = 180 – m 3
m2 = 180 – m  3
If the same number is subtracted from both sides of an
equation,
Then the new equation is equivalent to the original.
Substitution Property of
Equality
m 1 = m 2
Substitute (m 1) for (180 - m  3) in m2 = (180 - m 
3)
QED