Download - 7-1 Points, Lines, Planes, and Angles Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

7-1 Points, Lines, Planes, and Angles

Course 3

Warm Up

Problem of the Day

Lesson Presentation

Warm UpSolve.

1. x + 30 = 90

2. 103 + x = 180

3. 32 + x = 180

4. 90 = 61 + x

5. x + 20 = 90

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x = 60

x = 77

x = 148

x = 29

x = 70

Problem of the Day Mrs. Meyer’s class is having a pizza party. Half the class wants pepperoni on the pizza, of the class wants sausage on the pizza, and the rest want only cheese on the pizza. What fraction of Mrs. Meyer’s class wants just cheese on the pizza?

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Learn to classify and name figures.

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Vocabularypoint line plane

segment ray angle

right angle acute angle

obtuse angle complementary angles

supplementary angles

vertical angles

congruent

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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Additional 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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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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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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Check 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


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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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Additional 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, RQT

SQP, SQR

mTQP + mRQT = 47° + 133° = 180°

mSQP + mSQR = 137° + 43° = 180°

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A. Name a right angle in the figure.

BEC

E

D

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

E

D

CB

A 90° 75°15°


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D. Name a pair of complementary angles.

AEB, CED

E

D

CB

A 90° 75°15°


mAEB + mCED = 15° + 75° = 90°

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E. Name two pairs of supplementary angles.

AEB, BED

CED, AEC

E

D

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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Additional Example 3A: Finding the Measure of Vertical Angles

In 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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Additional Example 3B: Finding the Measure of 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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If m1 = 42°, find m3. 12

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Check It Out: Example 3A



m2 = 180° – 42° = 138°

m3 = 180° – 138° = 42°


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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

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Lesson QuizIn 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

Download - 7-1 Points, Lines, Planes, and Angles Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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