Post on 20-Jan-2016
Holt McDougal Geometry
3-1 Lines and Angles
Warm Up
Identify each of the following.
1. points that lie in the same plane
2. two angles whose sum is 180°
3. the intersection of two distinct intersecting lines
4. a pair of adjacent angles whose non-common sides are opposite rays
coplanar points
supplementary angles
point
linear pair
Holt McDougal Geometry
3-1 Lines and Angles
Identify parallel, perpendicular, and skew lines.
Identify the angles formed by two lines and a transversal.
Objectives
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Example 1: Identifying Types of Lines and Planes
Identify each of the following.
A. a pair of parallel segments
B. a pair of skew segments
C. a pair of perpendicular segments
D. a pair of parallel planes
LM ||QR
KN and PQ
NS SP
plane NMR || plane KLQ
Holt McDougal Geometry
3-1 Lines and Angles
Check It Out! Example 1
Identify each of the following.
a. a pair of parallel segments
b. a pair of skew segments
d. a pair of parallel planes
c. a pair of perpendicular segments
BF || EJ
BF and DE are skew.
BF FJ
plane FJH || plane BCD
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Example 2: Classifying Pairs of Angles
Give an example of each angle pair.
A. corresponding angles
B. alternate interior angles
C. alternate exterior angles
1 and 5
D. same-side interior angles
3 and 5
1 and 7
3 and 6
Holt McDougal Geometry
3-1 Lines and Angles
Check It Out! Example 2
Give an example of each angle pair.
A. corresponding angles
B. alternate interior angles
C. alternate exterior angles
1 and 3
D. same-side interior angles
2 and 7
1 and 8
2 and 3
Holt McDougal Geometry
3-1 Lines and Angles
To determine which line is the transversal for a given angle pair, locate the line that connects the vertices.
Helpful Hint
Holt McDougal Geometry
3-1 Lines and Angles
Example 3: Identifying Angle Pairs and Transversals
Identify the transversal and classify each angle pair.
A. 1 and 3
B. 2 and 6
C. 4 and 6
transversal l corr. s
transversal nalt. int s
transversal malt. ext s
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Students will…
Use the angles formed by a transversal to prove two lines are
parallel.
Objective
Holt McDougal Geometry
3-1 Lines and Angles
Remember!
Converse of a theorem is found by exchanging the hypothesis and
conclusion.
***The converse of a theorem is not automatically true.
If it is true, it must be stated as a postulate or proved as a separate
theorem.
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Use the given information and the theorems you have learned to show that r || s.
4 8
4 8 4 and 8 are alternate exterior angles.
r || s Conv. Of Alt. Ext. s Thm.
Holt McDougal Geometry
3-1 Lines and Angles
Use the given information and the postulates you have learned to show that l || m.
1 3 1 and 3 are corresponding angles.
ℓ || m Conv. of Corr. s Post.
Holt McDougal Geometry
3-1 Lines and Angles
Which postulate proves that ℓ || m?
m3 = (4x – 80)°,
m7 = (3x – 50)°, x = 30
m3 = 4(30) – 80 = 40 Substitute 30 for x.m7 = 3(30) – 50 = 40 Substitute 30 for x.
ℓ || m Conv. of Corr. s Post.3 7 Def. of s.
m3 = m7
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles
Holt McDougal Geometry
3-1 Lines and Angles