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