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3-1. Lines and Angles. Holt Geometry. Are You Ready?. Lesson Presentation. Lesson Quiz. 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 - PowerPoint PPT Presentation
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Holt Geometry
3-1 Lines and Angles3-1 Lines and Angles
Holt Geometry
Are You Are You Ready?Ready?Lesson PresentationLesson Presentation
Lesson QuizLesson Quiz
Holt 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 Geometry
3-1 Lines and Angles
Identify parallel, perpendicular, and skew lines.
Identify the angles formed by two lines and a transversal.
Objectives
Holt Geometry
3-1 Lines and Angles
parallel linesperpendicular linesskew linesparallel planestransversalcorresponding anglesalternate interior anglesalternate exterior anglessame-side interior angles
Vocabulary
Holt Geometry
3-1 Lines and Angles
Holt Geometry
3-1 Lines and Angles
Segments or rays are parallel, perpendicular, or skew if the lines that contain them are parallel, perpendicular, or skew.
Helpful Hint
Holt 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 Geometry
3-1 Lines and AnglesExample 2: Identifying Parallel,
Perpendicular, and Skew
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 Geometry
3-1 Lines and Angles
Holt Geometry
3-1 Lines and Angles
Example 3: 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 Geometry
3-1 Lines and Angles
Example 4
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 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 Geometry
3-1 Lines and Angles
Example 5: 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 Geometry
3-1 Lines and Angles
Example 6
Identify the transversal and classify the angle pair 2 and 5 in the diagram.
transversal nsame-side int. s.
Holt Geometry
3-1 Lines and Angles
Lesson Quiz: Part I
Identify each of the following.
1. a pair of parallel segments
2. a pair of skew segments
3. a pair of perpendicular segments
4. a pair of parallel planes
EH || FG
BF and EH
CG GH
ABC and EFG
Holt Geometry
3-1 Lines and Angles
Lesson Quiz: Part II
Identify each of the following.
5. one pair alternate interior angles
6. One pair corresponding angles
7. one pair alternate exterior angles
EHG and HGK
8. one pair same-side interior angles
EHG and FGJ
IHE and JGK
EHG and HGF