Warm Up
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3.1
Warm UpWarm Up
Lesson QuizLesson Quiz
Lesson PresentationLesson Presentation
Identify Pairs of Lines and Angles
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3.1 Warm-Up
ANSWER D
2. What is the intersection of AD and DB?
1. Name a line that does not intersect AD.
ANSWER BC
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3.1 Example 1
Think of each segment in the figure as part of a line. Which line(s) or plane(s) in the figure appear to fit the description?
a. Line(s) parallel to CD and containing point A
SOLUTION
AB , HG , and EF all appear parallel to CD , but only AB contains point A.
a.
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3.1 Example 1
Think of each segment in the figure as part of a line. Which line(s) or plane(s) in the figure appear to fit the description?
SOLUTION
b. Line(s) skew to CD and containing point A
Both AG and AH appear skew to CD and contain point A.
b.
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3.1 Example 1
Think of each segment in the figure as part of a line. Which line(s) or plane(s) in the figure appear to fit the description?
SOLUTION
c. BC, AD , DE , and FC all appear perpendicular to CD , but only AD contains point A.
c. Line(s) perpendicular to CD and containing point A
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3.1 Example 1
Think of each segment in the figure as part of a line. Which line(s) or plane(s) in the figure appear to fit the description?
SOLUTION
d. Plane(s) parallel to plane EFG and containing point A
d. Plane ABC appears parallel to plane EFG and contains point A.
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3.1 Example 2
Photography
The given line markings show how the roads are related to one another.
Name a pair of parallel lines.
a.
SOLUTION
a. MD FE
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3.1 Example 2
Photography
The given line markings show how the roads are related to one another.
SOLUTION
Name a pair of perpendicular lines.
b.
b. MD BF
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3.1 Example 2
Photography
The given line markings show how the roads are related to one another.
SOLUTION
Is FE AC ? Explain.c.
FE is not parallel to AC , because MD is parallel to FE and by the Parallel Postulate there is exactly one line parallel to FE through M.
c.
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3.1 Guided Practice
1. Look at the diagram in Example 1. Name the lines through point H that appear skew to CD.
ANSWER AH , EH
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3.1 Guided Practice
2. In Example 2, can you use the Perpendicular Postulate to show that AC is not perpendicular to BF ? Explain why or why not.
Yes; Since A is not on MD and MD is to BF, the Perpendicular Postulate guarantees that there is exactly one line through a point perpendicular to a line, so AC can not be perpendicular to BF also.
ANSWER
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3.1 Example 3
SOLUTION
a. ∠51and∠62and∠73and∠84and
b. ∠72and∠54and
c. ∠81and∠63and
Identify all pairs of angles of the given type.
d. ∠52and∠74and
a. Corresponding
b. Alternate interior
c. Alternate exterior
Consecutive interiord.
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3.1 Guided Practice
Classify the pair of numbered angles.
ANSWER
corresponding angles
3.
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3.1 Guided Practice
Classify the pair of numbered angles.
4.
ANSWER
alternate exterior angles.
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3.1 Guided Practice
Classify the pair of numbered angles.
5.
ANSWER
alternate interior angles.
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3.1 Lesson Quiz
1. Name the pairs of corresponding angles .
2. Name the pairs of alternate interior angles .
3. Name the pairs of consecutive interior angles .
ANSWER 2 and 7; 3 and 6
ANSWER 2 and 3; 6 and 7
ANSWER 1 and 3; 5 and 7;
2 and 4; 6 and 8
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3.1 Lesson Quiz
4. The figure shows a painting easel. Does AB appear to be parallel, perpendicular, or skew to CD?
ANSWER Parallel