Write a two-column proof for the situation in Example
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Write a two-column proof for the situation in Example 4 on page 107 . m ∠ 1 = m ∠ 3. GIVEN:. m ∠ EBA = m ∠ DBC. PROVE:. REASONS. STATEMENT . 1. 1. m ∠ 1 = m ∠ 3. Given. 2. Angle Addition Postulate. 2. m ∠ EBA = m ∠ 3 + m ∠ 2. 3.

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EXAMPLE 1

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Example 1

Write a two-column proof for the situation in Example 4 on page 107.

m∠ 1=m∠ 3

GIVEN:

m∠ EBA= m∠ DBC

PROVE:

REASONS

STATEMENT

1.

1.

m∠ 1=m∠ 3

Given

2.

Angle Addition Postulate

2.

m∠ EBA =m∠ 3 + m∠ 2

3.

Substitution Property of Equality

3.

m∠ EBA=m∠ 1 + m∠ 2

EXAMPLE 1

Write a two-column proof


Example 1

4.

Angle Addition Postulate

m∠ EBA= m∠ DBC

5.

5.

Transitive Property of Equality

EXAMPLE 1

Write a two-column proof

4.

m∠ 1 +m∠ 2 = m∠ DBC


Example 1

1. Four steps of a proof are shown. Give the reasons for the last two steps.

REASONS

STATEMENT

1.

1.

AC = AB + AB

Given

2.

2.

AB + BC = AC

Segment Addition Postulate

?

3.

3.

AB + AB = AB + BC

?

4.

4.

AB = BC

for Example 1

GUIDED PRACTICE

GIVEN :AC = AB + AB

PROVE :AB = BC


Example 1

ANSWER

GIVEN :AC = AB + AB

PROVE :AB = BC

REASONS

STATEMENT

1.

1.

AC = AB + AB

Given

2.

2.

AB + BC = AC

Segment Addition Postulate

3.

3.

AB + AB = AB + BC

Transitive Property of Equality

4.

4.

AB = BC

Subtraction Property of Equality

for Example 1

GUIDED PRACTICE


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