3.1 Lines and Angles
• Parallel Lines
– Coplanar lines that do not intersect.
– The symbol || means “is parallel to.”
AE || BF
AD || BC
3.1 Lines and Angles
• Skew Lines
– Are noncoplanar
– They are not parallel and do not intersect.
ABandCG
3.1 Lines and Angles
• Parallel Planes
– Planes that do not intersect.
planeABCD || planeEFGH
Identifying Nonintersecting Lines and Planes
•
A.
B.
C.
D.
In the figure, assume that lines and planes that appear
to be parallel are parallel.
Which segments are parallel to AB?
Which segments are skew to CD?
What are two pairs of parallel planes?
What are two segments parallel to plane BCGF?
Identifying Nonintersecting Lines and Planes
A.
EF , DC , and HG
B.
BF , AE , EH , and FG
C.
D.
planeABCD || planeEFGH
planeDCG || planeABF
ADand DH
Transversal
• A transversal is a line that intersects two or more coplanar
lines at distinct points.
• Angles 3, 4, 5, and 6 are lie inside of ℓ and m, so they are
interior angles.
• Angles 1, 2, 7, and 8 lie outside of ℓ and m, so they are exterior
angles.
Angle Pairs formed by Transversals
• Alternate Interior Angles
– Nonadjacent interior angles that lie on opposite
sides of the transversal.
3and 5
4and 6
Angle Pairs formed by Transversals
• Same-Side Interior Angles
– Interior angles that lie on the same side of the
transversal.
4and 5
3and 6
Angle Pairs formed by Transversals
• Corresponding Angles
– Corresponding angles lie on the same side of the
transversal t and are in corresponding positions.
1and 5
2and 6
3and 7
4and 8
Angle Pairs formed by Transversals
• Alternate Exterior Angles
– Nonadjacent exterior angles that lie on opposite
sides of the transversal.
1and 7
2and 8
Identifying an Angle Pair
• Name a pair of alternate interior angles.
3and 7
2and 6
Classifying an Angle Pair
• The photo shows the Royal Ontario Museum in Toronto,
Canada. Are angles 1 and 3 alternate interior angles, sameside interior angles, corresponding angles, or alternate exterior
angles?
• Corresponding Angles!
More Practice!!!!!
• Classwork – Textbook p. 144 #11 – 42
ALL!!
• Homework – Finish classwork.