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Warm Up

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Preview. Warm Up. California Standards. Lesson Presentation. QP,. PQ,. QP,. QR. QR. PQ. Warm Up Use the diagram to name each figure. P. Q. R. 1. three points. P, Q, R. 2. a line. plane PQR. 3. a plane. 4. three rays. 5. two segments. California Standards. - PowerPoint PPT Presentation
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Holt CA Course 1 8-2 Geometric Relationships Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson Presentation Preview Preview
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Page 1: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Warm UpWarm Up

California StandardsCalifornia Standards

Lesson PresentationLesson Presentation

PreviewPreview

Page 2: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Warm UpUse the diagram to name each figure.

P, Q, R1. three points

plane PQR

P

Q

R

PQ2. a line

3. a plane

4. three rays

5. two segments

PQ, QP, QR

QP,QR

Page 3: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

MG3.6 Identify elements of three-dimensional geometric objects (e.g., diagonals of rectangles solids) and describe how two or more objects are related in space (e.g., skew lines, the possible ways three planes might intersect).

California Standards

Page 4: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Vocabulary

parallel linesperpendicular linesskew linesparallel planesperpendicular planes

Page 5: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Parallel lines are lines in the same plane that never intersect.

Line WX is parallel to line YZ.

WX || YZ.

Page 6: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

The red arrows on lines WX and YZ show that the lines are parallel.

Reading Math

Page 7: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Perpendicular lines intersect to form 90o angles, or right angles.

Line RS is perpendicular to line TU.

RS | TU. __

Page 8: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Skew lines are lines that lie in different planes. They are neither parallel nor intersecting.

Line AB and line ML are skew lines.

AB and ML are skew.

Page 9: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Identify two lines that have the given relationship.

A. parallel lines

Additional Example 1: Identifying Lines in Space

The lines are in the same plane and do not intersect.

DC

BA

EAB || DC

Page 10: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Identify two lines that have the given relationship.

B. perpendicular lines

Additional Example 1: Identifying Lines in Space

The lines intersect to form 90o angles.

DC

BA

ECD | CE __

Page 11: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Two lines may be perpendicular even though they do not appear to be perpendicular. Use the markings on the drawings and read the problem carefully to determine which lines are perpendicular.

Caution!

Page 12: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Identify two lines that have the given relationship.

C. skew lines

Additional Example 1: Identifying Lines in Space

The lines lie in different planes. They are neither parallel nor intersecting.

DC

BA

E

AD and CE

Page 13: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Check It Out! Example 1

NP PS

Identify two lines that have the given relationship.

A. perpendicular lines

The lines insect to form 90o angles.

Page 14: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Check It Out! Example 1

NP and QR

Identify two lines that have the given relationship.

B. skew lines

The lines lie in different planes. They are neither parallel nor intersecting.

Page 15: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Check It Out! Example 1

NR and PS

Identify two lines that have the given relationship.

C. parallel lines

The lines are in the same plane and do not intersect.

Page 16: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Page 17: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Identify two planes that appear to have the given relationship.

A. perpendicular planes

Additional Example 2: Identifying Planes in Space

The planes intersect to form right angles.

M

J

K

N

Pplane MPL plane NPL

L

Page 18: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

A plane may be named by any three points that are not on the same line.

Remember!

Page 19: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Identify two planes that appear to have the given relationship.

B. parallel planes

Additional Example 2: Identifying Planes in Space

The planes do not intersect.

M

J

K

N

P

L

plane JKL || plane MNP.

Page 20: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Identify two planes that appear to have the given relationship.

C. neither perpendicular nor parallel planes

Additional Example 2: Identifying Planes in Space

The planes intersect, but they do not form right angles.

M

J

K

N

P

L

plane JMN and plane MPL.

Page 21: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Identify two planes that appear to have the given relationship.

A. perpendicular planes

Check It Out! Example 2

The planes intersect to form right angles.

plane BAC plane EAC

B

D

F

CA

E

Page 22: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Identify two planes that appear to have the given relationship.

B. parallel planes

Check It Out! Example 2

The planes do not intersect.

plane BAC || plane DEF

B

D

F

CA

E

Page 23: Warm Up

Holt CA Course 1

8-2 Geometric Relationships

Identify two planes that appear to have the given relationship.

C. neither perpendicular nor parallel planes

Check It Out! Example 2

The planes intersect, but they do not form right angles.

plane AEF and plane BDF

B

D

F

CA

E

Page 24: Warm Up

Holt CA Course 1

8-2 Geometric RelationshipsLesson Quiz: Part I

Identify two lines that have the given relationship.

1. parallel lines

2. perpendicular lines

3. neither perpendicular nor parallel

FK || EJ

FK KJ

FE and DH

Page 25: Warm Up

Holt CA Course 1

8-2 Geometric RelationshipsLesson Quiz: Part II

Identify two planes that appear to have the given relationship.

4. parallel planes

5. perpendicular planes

6. neither perpendicular nor parallel

plane SPQ || plane WTU

plane PSW plane WSR

plane PQU and plane RQU


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