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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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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

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.


Vocabulary

point line plane

segment ray angle

right angle

acute angle

obtuse angle

straight angle

complementary angles

supplementary angles


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


A geometry. Segments, rays, and angles are defined in terms of these basic figures.point names a location.

• A

Point A


C geometry. Segments, rays, and angles are defined in terms of these basic figures.

l

B

line l, or BC

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


A geometry. Segments, rays, and angles are defined in terms of these basic figures.plane is a perfectly flat surface that extends forever in all directions.

P

E

plane P, or plane DEF

D

F


GH geometry. Segments, rays, and angles are defined in terms of these basic figures.

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

H

G


A geometry. Segments, rays, and angles are defined in terms of these basic figures.ray is a part of a line that starts at one point and extends forever in one direction.

J

KJ

K


KL geometry. Segments, rays, and angles are defined in terms of these basic figures. 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.


Plane or plane geometry. Segments, rays, and angles are defined in terms of these basic figures.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.


JK, KL, LM, JM geometry. Segments, rays, and angles are defined in terms of these basic figures.

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.


Caution! geometry. Segments, rays, and angles are defined in terms of these basic figures.

When naming a ray always write the endpoint first.


AB, BC, CD, AD geometry. Segments, rays, and angles are defined in terms of these basic figures.

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.


B geometry. Segments, rays, and angles are defined in terms of these basic figures.

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.


B geometry. Segments, rays, and angles are defined in terms of these basic figures.

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


1 geometry. Segments, rays, and angles are defined in terms of these basic figures.

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.


Additional Example 2: Classifying Angles geometry. Segments, rays, and angles are defined in terms of these basic figures.

Use the diagram to name each figure.

A. a right angle

TQS

B. two acute angles

TQP, RQS


Reading Math geometry. Segments, rays, and angles are defined in terms of these basic figures.

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


Additional Example 2: Classifying Angles geometry. Segments, rays, and angles are defined in terms of these basic figures.

Use the diagram to name each figure.

C. two obtuse angles

SQP, RQT


Additional Example 2: Classifying Angles geometry. Segments, rays, and angles are defined in terms of these basic figures.

Use the diagram to name each figure.

D. a pair of complementary angles

TQP, RQS

mTQP + mRQS = 47° + 43° = 90°


Additional Example 2: Classifying Angles geometry. Segments, rays, and angles are defined in terms of these basic figures.

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


C geometry. Segments, rays, and angles are defined in terms of these basic figures.

B

90°

A

D

75°

15°

E

Check It Out! Example 2

Use the diagram to name each figure.

A. a right angle

BEC


C geometry. Segments, rays, and angles are defined in terms of these basic figures.

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


C geometry. Segments, rays, and angles are defined in terms of these basic figures.

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


C geometry. Segments, rays, and angles are defined in terms of these basic figures.

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


Possible answer: geometry. Segments, rays, and angles are defined in terms of these basic figures.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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