EDGE Math 8

Complete the two-column proof of the Same-Side Exterior Angles Theorem. Identify the missing statement or reason. Type the letter of your answer in each blank.

Given:	$l ∥ m$ cut by transversal n.
Prove:	$∠ 1$ and $∠ 7$ are supplementary

Choices:

a.	Same-Side Interior Angles Theorem
b.	$m ∠ 1 + m ∠ 7 = 360 ° - 180 °$
c.	$l ∥ m$ cut by transversal n.
d.	$m ∠ 3 + m ∠ 5 = 180 °$
e.	Linear Pair Postulate

f.	Subtraction Property of Equality
g.	$∠ 5$ and $∠ 7$ form a linear pair.
h.	$m ∠ 1 + m ∠ 7$ $= 180 ° + 180 ° - (m ∠ 3 + m ∠ 5)$
i.	Definition of supplementary angles
j.	$m ∠ 7 = 180 ° - m ∠ 5$

Proof:

Statements

Reasons

1. Given

∠ 1

and

∠ 3

form a linear pair.

2. Definition of linear pair

∠ 1

and

∠ 3

are supplementary.

∠ 5

and

∠ 7

are supplementary.

∠ 3

and

∠ 5

are supplementary.

m ∠ 1 + m ∠ 3 = 180 °

m ∠ 5 + m ∠ 7 = 180 °

5. Definition of supplementary angles

m ∠ 1 = 180 ° - m ∠ 3

6. Subtraction Property of Equality

7. Addition Property of Equality

8. Statements 5 and 7, and Substitution Property of Equality

m ∠ 1 + m ∠ 7 = 180 °

10.

∠ 1

and

∠ 7

are supplementary.

10.

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