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7-1 Points, Lines, Planes, and Angles

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Warm UpProblem of the DayLesson Presentation

Learn to classify and name figures.

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Vocabularypoint line planesegment ray angleright angle acute angleobtuse angle complementary anglessupplementary anglesvertical anglescongruent

Insert Lesson Title Here

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Points, lines, and planes are the building blocks of geometry. Segments, rays, and angles are defined in terms of these basic figures.

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A point names a location. • A Point A

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A line is perfectly straight and extends forever in both directions.

line l, or BCB

Cl

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A plane is a perfectly flat surface that extends forever in all directions.

plane P, or plane DEF

DE

F

PP

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G

HA segment, or line segment, is the part of a line between two points.

GH

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K

JA ray is a part of a line that starts at one point and extends forever in one direction.

KJ

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7-1 Points, Lines, Planes, and AnglesAdditional Example 1: Naming Points, Lines, Planes,

Segments, and Rays

A. Name 4 points in the figure.

B. Name a line in the figure.Point J, point K, point L, and point M

Any 2 points on a line can be used.KL or JK

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Segments, and Rays

C. Name a plane in the figure.

Plane , plane JKL Any 3 points in the plane that form a triangle can be used.

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Segments, and Rays

D. Name four segments in the figure.

E. Name four rays in the figure.KJ, KL, JK, LK

JK, KL, LM, JM

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7-1 Points, Lines, Planes, and AnglesCheck It Out: Example 1

A. Name 4 points in the figure.

B. Name a line in the figure.Point A, point B, point C, and point D

A B

CD

DA or BC Any 2 points on a line can be used.

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C. Name a plane in the figure.

Plane , plane ABC, plane BCD, plane CDA, or plane DAB

Any 3 points in the plane that form a triangle can be used.

A B

CD

Check It Out: Example 1

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D. Name four segments in the figure

E. Name four rays in the figureDA, AD, BC, CB

AB, BC, CD, DA

A B

CD


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An angle () is formed by two rays with a common endpoint called the vertex (plural, vertices). Angles can be measured in degrees. One degree, or 1°, is of a circle. m1 means the measure of 1. The angle can be named XYZ, ZYX, 1, or Y. The vertex must be the middle letter.

1360

X

Y Z1 m1 = 50°

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The measures of angles that fit together to form a straight line, such as FKG, GKH, and HKJ, add to 180°.

F K J

G H

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The measures of angles that fit together to form a complete circle, such as MRN, NRP, PRQ, and QRM, add to 360°.

P

R QM

N

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A right angle measures 90°. An acute angle measures less than 90°. An obtuse angle measures greater than 90° and less than 180°.Complementary angles have measures that add to 90°. Supplementary angles have measures that add to 180°.

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A right angle can be labeled with a small box at the vertex.

Reading Math

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7-1 Points, Lines, Planes, and AnglesAdditional Example 2: Classifying Angles

A. Name a right angle in the figure.

B. Name two acute angles in the figure.

TQS

TQP, RQS

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C. Name two obtuse angles in the figure.SQP, RQT

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D. Name a pair of complementary angles.

TQP, RQS mTQP + mRQS = 47° + 43° = 90°

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E. Name two pairs of supplementary angles.

TQP, RQTSQP, SQR

mTQP + mRQT = 47° + 133° = 180°mSQP + mSQR = 137° + 43° = 180°

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7-1 Points, Lines, Planes, and AnglesCheck It Out: Example 2

A. Name a right angle in the figure.BEC

ED

CB

A 90° 75°15°

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C. Name two obtuse angles in the figure.

BED, AEC

B. Name two acute angles in the figure.AEB, CED

ED

CB

A 90° 75°15°


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D. Name a pair of complementary angles.

AEB, CED

ED

CB

A 90° 75°15°


mAEB + mCED = 15° + 75° = 90°

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E. Name two pairs of supplementary angles.

AEB, BEDCED, AEC

ED

CB

A 90° 75°15°


mAEB + mBED = 15° + 165° = 180°

mCED + mAEC = 75° + 105° = 180°

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Congruent figures have the same size and shape.• Segments that have the same length are congruent.• Angles that have the same measure are congruent.• The symbol for congruence is , which is read “is congruent to.”Intersecting lines form two pairs of vertical angles. Vertical angles are always congruent, as shown in the next example.

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7-1 Points, Lines, Planes, and AnglesAdditional Example 3A: Finding the Measure of Vertical

AnglesIn the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.

If m1 = 37°, find m3.

The measures of 1 and 2 are supplementary.


m2 = 180° – 37° = 143°

m3 = 180° – 143° = 37°So m1 = m3 or m1 = m3. ~

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7-1 Points, Lines, Planes, and AnglesAdditional Example 3B: Finding the Measure of Vertical

AnglesIn the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.

If m4 = y°, find m2.

m3 = 180° – y°m2 = 180° – (180° – y°)

= 180° – 180° + y°= y°

Distributive Property m2 = m4

So m4 = m2 or m4 m2.

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In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.

If m1 = 42°, find m3. 12 3

4

Check It Out: Example 3A


The measures of 2 and 3 are supplementary.m2 = 180° – 42° = 138°

m3 = 180° – 138° = 42°So m1 = m3 or m1 m3.

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In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.

If m4 = x°, find m2.

m3 = 180° – x°m2 = 180° – (180° – x°)

= 180° –180° + x°= x°

Distributive Property m2 = m4

Check It Out: Example 3B

12 3

4

So m4 = m2 or m4 m2.

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7-1 Points, Lines, Planes, and AnglesLesson Quiz

In the figure, 1 and 3 are vertical angles, and 2 and 4 are vertical angles.1. Name three points in the figure.

3. Name a right angle in the figure.

4. Name a pair of complementary angles.

5. If m1 = 47°, then find m3.

2. Name two lines in the figure.Possible answer: A, B, and C

Possible answer: AGF

Possible answer: 1 and 2

47°

Possible answer: AD and BE

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