Warm Up

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# Warm Up - PowerPoint PPT Presentation

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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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

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.
C

l

B

line l, or BC

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

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

P

E

plane P, or plane DEF

D

F

GH

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

H

G

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

J

KJ

K

KL or JK

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

Use the diagram to name each figure.

A. a line

Any 2 points on a line can be used.

Plane or plane JKL

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

Use the diagram to name each figure.

B. a plane

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

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

Write the two points in any order.

D. four rays

Write the endpoint first.

Caution!

When naming a ray always write the endpoint first.

B

A

C

D

CB, CD, DA, DC

Check It Out! Example 1

Use the diagram to name each figure.

A. four segments

Write the two points in any order.

B. four rays

Write the endpoint first.

B

A

AB or DC

C

D

Check It Out! Example 1

Use the diagram to name each figure.

C. a line

Any 2 points on a line can be used.

B

A

C

D

Check It Out! Example 1

Use the diagram to name each figure.

D. a plane

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

Plane R or plane ABC

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.

Use the diagram to name each figure.

A. a right angle

TQS

B. two acute angles

TQP, RQS

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

Use the diagram to name each figure.

C. two obtuse angles

SQP, RQT

Use the diagram to name each figure.

D. a pair of complementary angles

TQP, RQS

mTQP + mRQS = 47° + 43° = 90°

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

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

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

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

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