Learning Objective: Identify and describe geometric figures Identify angles and angle pairs

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Geometry Presentation #1 Building Blocks of Geometry & Classifying Angles April 22, 2013 Math Block 4. Learning Objective: Identify and describe geometric figures Identify angles and angle pairs. Warm Up What geometry term might you associate with each object?

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### Geometry Presentation #1Building Blocks of Geometry & Classifying AnglesApril 22, 2013Math Block 4

Learning Objective:

Identify and describe geometric figures

Identify angles and angle pairs

Warm Up

What geometry term might you associate with each object?

1. one edge of a cardboard box

2. the floor

3. the tip of a pen

line segment or line

plane or rectangle

point

Vocabulary

point

line

plane

ray

line segment

congruent

XY, or YX, or l

X

Y

Use two points

on the line or a

lowercase letter to

name a line.

A number line is an example of a line.

A point is an exact

location. It is usually represented as a dot, but it has no size at all.

point A

Use a capital

letter to name

a point.

• A

l

A lineis a straight path that extends without end in opposite directions.

Q

S

R

A coordinate plane is an example of a plane.

A plane is a

Flat surface that

Has no thickness and extends forever.

plane QRS

Use three points

in any order, not

on the same line,

to name a plane.

Additional Example 1: Identifying Points, Lines, and Planes

Identify the figures in the diagram.

D

E

F

A. three points

D, E, and F

Choose any two points on a line to name the line.

B. two lines

DE, DF

Choose any three points, not on the same line, in any order.

C. a plane

plane DEF

Check It Out: Example 1

Identify the figures in the diagram.

G

H

I

F

A. four points

H, G, I, and F

Choose any two points on a line to name the line.

B. two lines

IH, HF

Choose any three points, not on the same line, in any order.

C. a plane

plane IGF

GH

Name the endpoint

first when naming

a ray.

G

H

LM, or ML

Use the endpoints

to name a line

segment.

L

M

A ray is a part of a line.

It has one endpoint and

extends forever

one direction.

A line segmentis

part of a line. or a ray

that extends from one

endpoint to another.

Additional Example 2: Identifying Line Segments and Rays

Identify the figures in the diagram.

M

N

O

A. three rays

Name the endpoint of a ray first.

MN, NM, MO

B. two line segments

Use the endpoints in any order to name a segment.

MN, MO

Check It Out: Example 2

Identify the figures in the diagram.

D

C

A. three rays

Name the endpoint of

a ray first.

B

A

BC, CA, BD

B. three line segments

Use the endpoints in any order to name a segment.

BA, CA, BD

Figures are congruent if they have the same shape and size. Line segments are congruent if they have the same length.

You can use tick marks to indicate congruent line

segments. In the triangle below, line segments AB and BC are congruent.

AB CD

ACBD

BF DF EC AE

The symbol means “is congruent to.”

Additional Example 3: Identifying Congruent Line Segments

Identify the line segments that are congruent in the figure.

One tick mark

Two tick marks

Three tick marks

A

AB AC

BCDE

B

C

BD CE

E

D

Check It Out: Example 3

Identify the line segments that are congruent in the figure.

One tick mark

Two tick marks

Three tick marks

Lesson Quizzes

Standard Lesson Quiz

Lesson Quiz for Student Response Systems

AG GD, GB GE

Lesson Quiz

Identify the figures in the diagram.

1. lines

2. plane

3. three rays

4. four line segments

5. Identify the line segments that are congruent in the figure.

Lesson Quiz for Student Response Systems

1. Identify the lines in the diagram.

A.

B.AB, AE

C.

D.

Lesson Quiz for Student Response Systems

2. Identify a plane in the diagram.

A. plane AFD

B. plane EFC

C. plane ABC

D. plane BGF

Lesson Quiz for Student Response Systems

3. Identify three rays in the diagram.

A.

B.

C.

D.

Lesson Quiz for Student Response Systems

4. Identify the line segments that are congruent in the figure.

A.

B.

C.

D.

Vocabulary

angle

vertex

right angle

acute angle

obtuse angle

straight angle

complementary angles

supplementary angles

A

Vertex

1

B

C

An angleis formed by two rays with a common endpoint. The two rays are the sides of the angle. The common endpoint is the vertex.

Angles are measured in degrees (°).

An angle’s measure determines the type of

angle it is.

A right angle is an angle that

that measures exactly 90°. The

symbol indicates a right angle.

An acute angle is an angle

that measures less than 90°.

Anobtuse angle is an angle

that measures more than 90°

but less than 180°.

A straightangle is an angle

that measures exactly 180°.

Tell whether each angle is acute, right, obtuse or straight.

A.

B.

acute angle

obtuse angle

You can name this angle ABC, CBA, B, or 1.

A •

1

B •

• C

Check It Out: Example 1

Tell whether each angle is acute, right, obtuse, or straight.

B.

A.

straight angle

acute angle

If the sum of the measures of two angles is

90°, then the angles are complementary

angles. If the sum of the measures of two

angles is 180°, then the angles are

supplementary angles.

To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° -75° = 30°. mOMP = 60°.

P

Q

O

N

R

M

Additional Example 2A: Identifying Complementary and Supplementary Angles

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

OMP and PMQ

Since 60° + 30° = 90°, PMQ andOMP are complementary.

If the angle you are measuring appears obtuse, then its measure is greater than 90°. If the angle is acute, its measure is less than 90°.

P

Q

O

Read mNMO as “the measure of angle NMO.”

N

R

M

Additional Example 2B: Identifying Complementary and Supplementary Angles

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

NMO and OMR

mNMO = 15° and mOMR = 165°

Since 15° + 165° = 180°, NMO andOMR are supplementary.

To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° -75° = 30°. mQMR = 75°.

P

Q

O

N

R

M

8-2

Additional Example 2C: Identifying Complementary and Supplementary Angles

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

PMQ and QMR

Since 30° + 75° = 105°, PMQ andQMR are neither complementary nor supplementary.

D

E

C

F

B

A

Check It Out: Example 2A

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

BAC and CAF

mBAC = 35° and mCAF = 145°

Since 35° + 145° = 180°, BAC andCAF are supplementary.

To find mCAD start with the measure that DA crosses, 90°, and subtract the measure that CA crosses, 35°. mCAD = 90° -35° = 55°. mEAF = 35°.

D

E

C

F

B

A

Check It Out: Example 2B

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

Since 55° + 35° = 90°, CAD andEAF are complementary.

D

E

C

F

B

A

Check It Out: Example 2C

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

BAC and EAF

mBAC = 35° and mEAF = 35°

Since 35° + 35° = 70°, BAC andEAF are neither supplementary nor complementary.

Additional Example 3: Finding Angle Measures

Angles A and B are complementary. If mA is 56°, what is the mB?

Since A and B are complementary, mA + mB = 90°.

mA + mB = 90°

56° + mB = 90°

Substitute 56° for mA.

Subtract 56° from both sides.

– 56° – 56°

mB = 34°

The measure of B = 34°.

Check It Out: Example 3

Angles P and Q are supplementary. If mP is 32°, what is the mQ?

Since P and Q are supplementary, mP + mQ = 180°.

mP + mQ = 180°

32° + mQ = 180°

Substitute 32° for mP.

Subtract 32° from both sides..

– 32°– 32°

mQ = 148°

The measure of Q = 148°.

Lesson Quizzes

Standard Lesson Quiz

Lesson Quiz for Student Response Systems

2.

Lesson Quiz: Part I

Tell whether each angle is acute, right, obtuse, or straight.

straight

1.

obtuse

Lesson Quiz: Part II

Use the diagram to tell whether the angles are complementary, supplementary, or neither.

3. AZB and BZC

neither

complementary

4. BZC and CZD

5. Angles M and N are supplementary. If mM is 117°, what is mN?

63°

Lesson Quiz for Student Response Systems

1. Identify the type of the given angle.

A. acute

B. obtuse

C. right

D. straight

Lesson Quiz for Student Response Systems

2. Identify the type of the given angle.

A. acute

B. obtuse

C. right

D. straight

Lesson Quiz for Student Response Systems

3. Use the diagram to identify the type of the given pair of angles. mAOB and mBOD

A. complementary

B. supplementary

C. right

D. none

Lesson Quiz for Student Response Systems

4. Angles A and B are complementary. If mA is 36°, what is mB?

A.54°

B.90°

C.126°

D.144°