1. Given: A, B, and C are collinear; AB = BC; AC = 20.
Prove: B is the midpoint of AC.
Statements:
1. A, B, and C are collinear.
2. AB = BC.
3. AC = 20.
4. AB + BC = AC.
5. AB + AB = 20.
6. 2AB = 20.
7. AB = 10.
8. BC = 10.
9. AB = BC = 10.
10. B is the midpoint of AC.
Reasons:
1. Given.
2. Given.
3. Given.
4. Segment Addition Postulate.
5. Substitution (from 2 and 4).
6. Simplify.
7. Division Property of Equality.
8. Substitution (from 2 and 7).
9. Transitive Property.
10. Definition of Midpoint.
2. Given: AB = CD and BC = DE.
Prove: AC = CE.
Statements:
1. AB = CD.
2. BC = DE.
3. AC = AB + BC.
4. CE = CD + DE.
5. AC = CD + DE.
6. AC = CE.
Reasons:
1. Given.
2. Given.
3. Segment Addition Postulate.
4. Segment Addition Postulate.
5. Substitution (from 1 and 3 into 4).
6. Transitive Property.
3. Given: AB = CD.
Prove: AC = BD.
Statements:
1. AB = CD.
2. AC = AB + BC.
3. BD = BC + CD.
4. AC = CD + BC.
5. AC = BD.
Reasons:
1. Given.
2. Segment Addition Postulate.
3. Segment Addition Postulate.
4. Substitution (from 1 and 2 into 3).
5. Commutative Property and Transitive Property.
Parent Tip: Review the logic above to help your child master the concept of angle proofs worksheet.
