EXAMPLE 1
Write a two-column proof
Write a two-column proof for
the situation in Example 4 on
page 107.
GIVEN: m 1 = m 3
PROVE: m EBA = m DBC
STATEMENT
1. m 1 = m 3
REASONS
1. Given
2. m EBA = m 3 + m 22. Angle Addition Postulate
3. m EBA = m 1 + m 23. Substitution Property of Equality
EXAMPLE 1
Write a two-column proof
4. m 1 + m 2 = m DBC4. Angle Addition Postulate
5. m EBA = m DBC
5. Transitive Property of Equality
GUIDED PRACTICE
1.
for Example 1
Four steps of a proof are shown. Give the reasons
for the last two steps.
GIVEN : AC = AB + AB
PROVE : AB = BC
STATEMENT
REASONS
1. AC = AB + AB
1. Given
2. AB + BC = AC
2. Segment Addition Postulate
3. AB + AB = AB + BC
3. ?
4. AB = BC
4. ?
GUIDED PRACTICE
for Example 1
ANSWER
GIVEN : AC = AB + AB
PROVE : AB = BC
STATEMENT
REASONS
1. AC = AB + AB
1. Given
2. AB + BC = AC
2. Segment Addition Postulate
3. AB + AB = AB + BC
3. Transitive Property of Equality
4. AB = BC
4. Subtraction Property of Equality