Section 10.1 : Lines and Angles Learning Targets: G.CO.1 and Prepares for G.CO.9 Important Terms and Definitions Parallel Lines : coplanar lines that do not intersect. The symbol ∥ means parallel to. Parallel Planes : are planes that do not intersect. (ex) The top and bottom of a box. Skew Lines : Lines that do not intersect and are not parallel. Transversal : a line that intersects two or more coplanar lines at distinct points. The diagram below shows the eight angles that are formed by a transversal t and two lines l and m. 1 2 m 3 4 5 6 Interior l 7 8 t Alternate Interior Angles : are nonadjacent interior angles that lie on opposite sides of the transversal. ∠3 and ∠6 ∠4 and ∠5 Same-Side Interior Angles : are interior angles that lie on the same-side of the transversal. ∠3 and ∠5 ∠4 and ∠6 Corresponding Angles : lie on the same side of the transversal and are in the same positions. ∠1 and ∠5 ∠3 and ∠7 ∠2 and ∠6 ∠4 and ∠8 Alternate Exterior Angles : are nonadjacent exterior angles that lie on opposite sides of the transversal. ∠1 and ∠8 ∠2 and ∠7
Transcript
Section 10.1 : Lines and Angles
Learning Targets: G.CO.1 and Prepares for G.CO.9
Important Terms and Definitions
Parallel Lines : coplanar lines that do not intersect. The symbol ∥ means parallel to.
Parallel Planes : are planes that do not intersect. (ex) The top and bottom of a box.
Skew Lines : Lines that do not intersect and are not parallel.
Transversal : a line that intersects two or more coplanar lines at distinct points. The diagram below shows the eight angles that are formed by a transversal t and two lines l and m.
1 2 m
3 4
5 6 Interior l
7 8
t
Alternate Interior Angles : are nonadjacent interior angles that lie on opposite sides of the transversal.
∠3 and ∠6 ∠4 and ∠5
Same-Side Interior Angles : are interior angles that lie on the same-side of the transversal.
∠3 and ∠5 ∠4 and ∠6
Corresponding Angles : lie on the same side of the transversal and are in the same positions.
∠1 and ∠5 ∠3 and ∠7 ∠2 and ∠6 ∠4 and ∠8
Alternate Exterior Angles : are nonadjacent exterior angles that lie on opposite sides of the transversal.
∠1 and ∠8 ∠2 and ∠7
Identifying Nonintersecting Lines and Planes
(ex 1) Use the figure below to answer the following:
Identifying and Classifying Angle Pairs
(ex 2) Use the figure below to fill in the angle pairs:
(ex 4) Identify all of the pairs of vertical angles in the figure from Example 2.
(ex 5) Draw a set of lines with a transversal where angles 3 and 6 are alternate interior angles and angles 4 and 7 are corresponding angles.
(ex 6) Name the two lines and the transversal that form each pair of angles. Then classify the pair of angles.
a) ∠1 and ∠4
b) ∠2 and ∠3
c) ∠𝑃𝑆𝑅 and ∠5
Homework – Section 10.1 : Lines and Angles
Use the figure below to identify the given types of angles.
1. 4 pairs of corresponding angles 2. 2 pairs of same-side interior angles 3. 2 pairs of alternate interior angles 4. 2 pairs of alternate exterior angles 5. 4 pairs of vertical angles
Use the figure below to identify the segments and planes that are described.
6. Segments that are parallel to 𝐶𝐵̅̅ ̅̅ 7. A pair of parallel planes 8. Two segments parallel to plane ABEF 9. Segment that is skew to 𝐺𝐹̅̅ ̅̅
In the figure below, assume that lines and planes that appear to be parallel are parallel. Use the figure to decide whether each statement below is true or false.
10. 𝐶𝐷 ⃡ ∥ 𝐻𝐺 ⃡ 11. plane 𝐴𝐸𝐷 ∥ plane 𝐹𝐺𝐻 12. 𝐴𝐵 ⃡ and 𝐻𝐺 ⃡ are skew lines 13. 𝐴𝐸 ⃡ and 𝐵𝐶 ⃡ are skew lines
14. Draw a transversal cutting through three lines. Number each angle. Then list all pairs of: a) alternate interior angles c) corresponding angles b) vertical angles d) alternate exterior angles
15. The letter Z illustrates alternate interior angles. Find at least two other letters that
illustrate pairs of angles that we discussed in today’s lesson. Draw the letters, then mark and describe the angle pairs.
16. You and a friend are driving go-karts on two different tracks. As you drive on a straight section heading east, your friend passes above you on a straight section heading south. Are these sections of the two tracks parallel, skew, or neither? Explain.
