learning objective: identify and describe geometric figures identify angles and angle pairs

GEOMETRY PRESENTATION #1BUILDING BLOCKS OF GEOMETRY & CLASSIFYING ANGLESAPRIL 22, 2013MATH BLOCK 4Learning Objective:

Identify and describe geometric figures

Identify angles and angle pairs

Warm UpWhat 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

pointlineplanerayline segmentcongruent

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

• A point AUse a capital letter to namea point.

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

A number line is an example of a line.

Helpful Hint

XY, or YX, or lUse two pointson the line or a lowercase letter to name a line.

X Y

l

A plane is a Flat surface that Has no thickness and extends forever.

plane QRSUse three pointsin any order, noton the same line,to name a plane.

A coordinate plane is an example of a plane.

Helpful Hint

Q

R

S

Identify the figures in the diagram.

Additional Example 1: Identifying Points, Lines, and Planes

DE

F

A. three points

B. two lines

C. a plane

D, E, and F

DE, DF

plane DEF

Choose any two points on a line to name the line.Choose any three points, not on the same line, in any order.

Check It Out: Example 1

HI

A. four points

B. two lines

C. a plane

H, G, I, and F

IH, HF

plane IGF

Identify the figures in the diagram.

G

Choose any two points on a line to name the line.Choose any three points, not on the same line, in any order.

F

A ray is a part of a line.It has one endpoint andextends foreverone direction.

GHName the endpointfirst when naminga ray.

A line segment is part of a line. or a raythat extends from oneendpoint to another.

LM, or MLUse the endpointsto name a line segment.

L M

HG

Identify the figures in the diagram.

Additional Example 2: Identifying Line Segments and Rays

M N

O

A. three rays

B. two line segments

MN, NM, MO

MN, MO

Name the endpoint of a ray first.

Use the endpoints in any order to name a segment.

Identify the figures in the diagram.

C

AB

D

Check It Out: Example 2

A. three rays

B. three line segments

BC, CA, BD

BA, CA, BD

Name the endpoint ofa ray first.

Use the endpoints in any order to name a segment.

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.

Identify the line segments that are congruent in the figure.

Additional Example 3: Identifying Congruent Line Segments

AB CD

AC BD

BF DF EC AE

One tick mark

Two tick marks

Three tick marks

The symbol means “is congruent to.”

Reading Math

Check It Out: Example 3

Identify the line segments that are congruent in the figure.

AB AC

BC DE

BD CE

One tick mark

Two tick marks

Three tick marks

A

B C

D E

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Lesson Quiz

Identify the figures in the diagram.

1. lines

2. planePossible answer: plane ABG

3. three rays

Possible answer: GA, GB, GC

4. four line segments Possible answer: AG, AD, DG, BG

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

AD, BE, CF

AG GD, GB GE

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.

Lesson Quiz for Student Response Systems

Vocabularyanglevertexright angleacute angleobtuse anglestraight anglecomplementary anglessupplementary angles

An angle is 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 (°).

A

CB

1

Vertex

An angle’s measure determines the type of angle it is.

A right angle is an angle that that measures exactly 90°. Thesymbol indicates a right angle.An acute angle is an anglethat measures less than 90°.

An obtuse angle is an anglethat measures more than 90°but less than 180°.

A straight angle is an anglethat measures exactly 180°.

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

Additional Example 1: Classifying Angles

A. B.

obtuse angle acute angle

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

Reading Math

A •

B • • C

1

Check It Out: Example 1

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

A. B.

straight angle acute angle

If the sum of the measures of two angles is90°, then the angles are complementary angles. If the sum of the measures of twoangles is 180°, then the angles are supplementary angles.

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

Additional Example 2A: Identifying Complementary and Supplementary Angles

OMP and PMQ

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

N

P Q

RM

To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° - 75° = 30°. mOMP = 60°.

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°.

Reading Math

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

Additional Example 2B: Identifying Complementary and Supplementary Angles

NMO and OMR

mNMO = 15° and mOMR = 165°

O

N

P Q

RM

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

Read mNMO as “the measure of angle NMO.”

Reading Math

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

Additional Example 2C: Identifying Complementary and Supplementary Angles

8-2

PMQ and QMR

O

N

P Q

RM

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

To find mPMQ start with the measure that QM crosses, 105°, and subtract the measure that MP crosses, 75°. mPMQ = 105° - 75° = 30°. mQMR = 75°.

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

Check It Out: Example 2A

BAC and CAF

mBAC = 35° and mCAF = 145°

C

B

D

E

FA

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

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

Check It Out: Example 2B

CAD and EAF

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

C

B

D

E

FA

To find mCAD start with the measure that DA crosses, 90°, and subtract the measure that CA crosses, 35°. mCAD = 90° - 35° = 55°. mEAF = 35°.

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

Check It Out: Example 2C

BAC and EAF

mBAC = 35° and mEAF = 35°

C

B

D

E

FA

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

Angles A and B are complementary. If mA is 56°, what is the mB?

Additional Example 3: Finding Angle Measures

Since A and B are complementary, mA + mB = 90°.

mA + mB = 90°

56° + mB = 90°

– 56° – 56°

mB = 34°

Substitute 56° for mA.

Subtract 56° from both sides.

The measure of B = 34°.

Angles P and Q are supplementary. If mP is 32°, what is the mQ?

Check It Out: Example 3

Since P and Q are supplementary, mP + mQ = 180°.

mP + mQ = 180°

32° + mQ = 180°

– 32° – 32°

mQ = 148°

Substitute 32° for mP.

Subtract 32° from both sides..

The measure of Q = 148°.

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

Lesson Quiz: Part ITell whether each angle is acute, right, obtuse, or straight.

1. straight

obtuse2.

Lesson Quiz: Part IIUse the diagram to tell whether the angles are complementary, supplementary, or neither.

3. AZB and BZC neither

4. BZC and CZD complementary

5. Angles M and N are supplementary. If mM is 117°, what is mN? 63°

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. mAOB and mBOD

A. complementary

B. supplementary

C. right

D. none

Lesson Quiz for Student Response Systems

4. Angles A and B are complementary. If mA is 36°, what is mB?

A. 54°

B. 90°

C. 126°

D. 144°

Lesson Quiz for Student Response Systems