Download 3-3 Parallel and Perpendicular Lines

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Parallel and Perpendicular Lines
Additional Examples
Suppose that the top and bottom pieces of a picture frame are
cut to make 60° angles with the exterior sides of the frame. At what
angle should the two sides be cut to ensure that opposite sides of the
frame will be parallel?
In order for the opposite sides of the frame to be parallel,
same-side interior angles must be supplementary.
Two 90° angles are supplementary, so find an adjacent angle that,
together with 60°, will form a 90° angle: 90° – 60° = 30°.
Quick Check
Parallel and Perpendicular Lines
Additional Examples
Study what is given, what you are to prove, and the
diagram. Then write a paragraph proof.
Given: In a plane, a  s, c  s, and a  b.
Prove: c  b
Proof: Lines a and c are both perpendicular to line s, so a  c because
two lines perpendicular to the same line are parallel. It is given that
a  b. Therefore , c  b because two lines parallel to the same line are
parallel to each other.
Quick Check