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Proving Lines Parallel
Lesson 3-2
Geometry
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 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.
2
Proving Lines Parallel
Lesson 3-2
Geometry
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
Divide each side by 2.
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 and AB and CD are parallel.
Geometry