MathMatters 3
Chapter 3
Lesson 3-7
Example 1
Given
∠ABC and ∠EBD are vertical angles.
Prove
m∠ABC = m∠EBD
Solution
Statements
1. ∠ABC and ∠EBD are vertical angles.
2. m∠ABC + m∠CBE = 180°
m∠EBD + m∠CBE = 180°
3. m∠ABC + m∠CBE = m∠EBD + m∠CBE
4. m∠ABC = m∠EBD
Reasons
1. Given
2. Angle Addition Postulate
3. Transitive Property of Equality
4. Addition Property of Equality
Example 2
SURVEYING Two parallel property lines are cut by a third line. How can the surveyor
know that m∠1 = m∠2?
Given
n || k
Prove
m∠1 = m∠2
Solution
Statements
1. n || k
2. m∠1 = m∠3
3. m∠2 = m∠3
4. m∠1 = m∠2
Reasons
1. Given
2. Parallel Line Postulate
3. Vertical Angle Theorem
4. Transitive Property of Equality
MathMatters 3
Chapter 3
Example 3
CARPENTRY A cross-brace is nailed to two wooden beams so that the alternate interior
angles formed are equal in measure. How can the carpenter know that the beams are parallel?
Given
m∠1 = m∠2
Prove
n || k
Solution
Statements
1. m∠1 = m∠2
2. m∠2 = m∠3
3. m∠1 = m∠3
4. n || k
Reasons
1. Given
2. Vertical Angle Theorem
3. Transitive Property of Equality
4. Corresponding Angles Theorem