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UNIT 3:
In this unit, we will be working with lines and angles.
Solve for the variables in each diagram.
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3.1 Parallel Lines and Transversals
What are parallel lines?
What are perpendicular lines?
Which are COPLANAR?
Are there lines that don’t intersect and AREN’T parallel?
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Definitions
Definition
Diagrams
How to Name It
Parallel lines are coplanar lines that do not intersect. The symbol || means “is parallel to.”
are parallel lines.
Symbols:
Skew lines are noncoplanar; they are not parallel and do not intersect.
are skew lines
Parallel planes are planes that do not intersect.
Planes P and Q are parallel planes.
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4. Identifying Lines and Planes That Do Not Intersect
Recall that each segment in the figure shown is part of a line, as shown for Answer the questions based on the appearance of the figure. a. Which line(s) are parallel to b. Which line(s) are skew to and also pass through point A? c. Name any line(s) perpendicular to d. Name any plane(s) parallel to plane CDHG.
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5. Identifying Lines and Planes That Do Not Intersect
Solution a. Which line(s) are parallel to b. Which line(s) are skew to and also pass through point A? c. Name any line(s) perpendicular to d. Name any plane(s) parallel to plane CDHG.
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Definition
Two segments are parallel if the lines containing them are parallel.
Parallel segments because / || m.
Nonparallel segments because the extended lines or segments themselves intersect.
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Definitions
A transversal is a line that intersects two or more coplanar lines at different points. The figure below shows the eight angles formed by a transversal t and two lines / and m.
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Definitions
Angles 3, 4, 5, and 6 lie between l and m. They are interior angles. Angles 1, 2, 7, and 8 lie outside of l and m. They are exterior angles.
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Definitions
Alternate interior angles are nonadjacent interior angles that lie on opposite sides of the transversal.
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Definitions
Same-side interior angles are interior angles that lie on the same side of the transversal (sometimes called consecutive interior angles).
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Definitions
Corresponding angles lie on the same side of the transversal and in corresponding positions.
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Definitions
Alternate exterior angles are nonadjacent exterior angles that lie on opposite sides of the transversal.
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13. Identifying Angle Pairs
List all angle pairs in the figure. a. alternate interior b. corresponding Solution a.
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14. Classifying an Angle Pair
The photo shows the Hearst Building in New York City. The new tower (showing many triangles) was completed in Fill in the blank. a. 1 and 5 are _____________ angles. b. 2 and 7 are _____________ angles.
alternate exterior
same-side interior
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