Transcript Proving Lines Parallel LESSON 3-2 Additional Examples Use the diagram above. Which lines, if any, must be parallel if are supplementary? It is given that 3

Proving Lines Parallel
LESSON 3-2
Additional Examples
Use the diagram above. Which lines, if any, must be parallel if
are supplementary?
It is given that
3 and
The diagram shows that
3 and
2
2 are supplementary.
4 and
2 are supplementary.
Because supplements of the same angle are congruent
(Congruent Supplements Theorem), 3
4.
Because 3 and 4 are congruent corresponding angles, EC || DK
by the Converse of the Corresponding Angles Postulate.
Quick Check
HELP
GEOMETRY
Proving Lines Parallel
LESSON 3-2
Additional Examples
Find the value of x for which
|| m.
The labeled angles are alternate interior angles.
If || m, the alternate interior angles are congruent,
and their measures are equal.
Write and solve the equation 5x – 66 = 14 + 3x.
5x – 66 = 14 + 3x
5x = 80 + 3x
Add 66 to each side.
2x = 80
Subtract 3x from each side.
x = 40
HELP
Divide each side by 2.
Quick Check
GEOMETRY
Proving Lines Parallel
LESSON 3-2
Additional Examples
A rectangular wooden frame has a diagonal metal
brace. The angles indicated were measured to be equal.
Which sides are parallel? Explain.
The top and bottom sides, or AB and CD, are parallel. By the
Converse of the Alternate Interior Angles Theorem, the lines that
contain AB and CD are parallel.
Quick Check
HELP
GEOMETRY