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Preview. Warm Up. California Standards. Lesson Presentation. Warm Up Solve. 1. x + 30 = 90 2. 103 + x = 180 3. 32 + x = 180 4. 90 = 61 + x 5. x + 20 = 90. x = 60. x = 77. x = 148. x = 29. x = 70. California Standards.

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slide1
Preview

Warm Up

California Standards

Lesson Presentation

slide2
Warm Up

Solve.

1. x + 30 = 90

2. 103 + x = 180

3. 32 + x = 180

4. 90 = 61 + x

5. x + 20 = 90

x = 60

x = 77

x = 148

x = 29

x = 70

slide3
California

Standards

Preparation for MG3.1 Identify and construct basic elements of geometric figures (e.g., altitudes, midpoints, diagonals, angle bisectors, and perpendicular bisectors; central angles, radii, diameters, and chords of circles) by using a compass and straightedge.

slide4
Vocabulary

point line plane

segment ray angle

right angle

acute angle

obtuse angle

straight angle

complementary angles

supplementary angles

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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.
slide7
C

l

B

line l, or BC

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

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

P

E

plane P, or plane DEF

D

F

slide9
GH

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

H

G

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

J

KJ

K

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KL or JK

Additional Example 1: Naming Lines, Planes, Segments, and Rays

Use the diagram to name each figure.

A. a line

Possible answers:

Any 2 points on a line can be used.

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Plane or plane JKL

Additional Example 1: Naming Lines, Planes, Segments, and Rays

Use the diagram to name each figure.

B. a plane

Possible answers:

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

slide13
JK, KL, LM, JM

KJ, KL, JK, LK

Additional Example 1: Naming Lines, Planes, Segments, and Rays

Use the diagram to name each figure.

C. four segments

Possible answers:

Write the two points in any order.

D. four rays

Possible answers:

Write the endpoint first.

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Caution!

When naming a ray always write the endpoint first.

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AB, BC, CD, AD

B

A

C

D

CB, CD, DA, DC

Check It Out! Example 1

Use the diagram to name each figure.

A. four segments

Possible answers:

Write the two points in any order.

B. four rays

Possible answers:

Write the endpoint first.

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B

A

AB or DC

C

D

Check It Out! Example 1

Use the diagram to name each figure.

C. a line

Possible answers:

Any 2 points on a line can be used.

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B

A

C

D

Check It Out! Example 1

Use the diagram to name each figure.

D. a plane

Possible answers:

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

Plane R or plane ABC

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1

360

An angle () is formed by two rays, or sides, with a common endpoint called the vertex. You can name an angle several ways: by its vertex, by its vertex and a point on each ray, or by a number. When three points are used, the middle point must be the vertex.

Angles are usually measured in degrees ((°). Since

there are 360° in a circle, one degree is of a circle.

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Additional Example 2: Classifying Angles

Use the diagram to name each figure.

A. a right angle

TQS

B. two acute angles

TQP, RQS

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Reading Math

mTQS is read as “the measure of angle TQS.”

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Additional Example 2: Classifying Angles

Use the diagram to name each figure.

C. two obtuse angles

SQP, RQT

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Additional Example 2: Classifying Angles

Use the diagram to name each figure.

D. a pair of complementary angles

TQP, RQS

mTQP + mRQS = 47° + 43° = 90°

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Additional Example 2: Classifying Angles

Use the diagram to name each figure.

E. two pairs of supplementary angles

TQP, RQT

mTQP + mRQT = 47° + 133° = 180°

mSQP + mSQR = 137° + 43° = 180°

SQP, SQR

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C

B

90°

A

D

75°

15°

E

Check It Out! Example 2

Use the diagram to name each figure.

A. a right angle

BEC

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C

B

90°

A

D

75°

15°

E

Check It Out! Example 2

Use the diagram to name each figure.

B. two acute angles

AEB, CED

C. two obtuse angles

BED, AEC

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C

B

90°

A

D

75°

15°

E

Check It Out! Example 2

Use the diagram to name each figure.

D. a pair of complementary angles

mAEB + mCED = 15° + 75° = 90°

AEB, CED

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C

B

90°

A

D

75°

15°

E

Check It Out! Example 2

Use the diagram to name each figure.

E. two pairs of supplementary angles

mAEB + mBED = 15° + 165° = 180°

AEB, BED

mCED + mAEC = 75° + 105° = 180°

CED, AEC

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Possible answer: AD and BE

Lesson Quiz

1. Name two lines in the figure.

2. Name a right angle in the figure.

Possible answer: AGF

3. Name a pair of complementary angles.

Possible answer: 1 and 2

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