Do Now 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.

Do NowWhat 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

Course 2

8-1 Building Blocks of Geometry

Hwk p 68 & 69 THIS SHOULD BE A REVIEW

EQ: How do I identify / describe the building blocks of geometry and identify angles?

Course 2

8-1 Building Blocks of Geometry

M7P1.a Build new mathematical knowledge through problem solving; M7P1.b Solve problems that arise inmathematics and in other contexts;

Review %

A point is an exact location in space. 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 YXUse two pointson the line to name a line.

X Y

Course 2

8-1 Building Blocks of Geometry

A plane is a perfectly flatsurface that extends infinitelyin all directions.

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

Course 2

8-1 Building Blocks of Geometry

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.

Course 2

8-1 Building Blocks of Geometry

Check It Out: Example 1

Insert Lesson Title Here

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

Course 2

8-1 Building Blocks of Geometry

A ray is a part of a line.It has one endpoint andextends without end inone 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

Course 2

8-1 Building Blocks of Geometry

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.

Course 2

8-1 Building Blocks of Geometry

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.

Course 2

8-1 Building Blocks of Geometry

Figures are congruent if they have the same shape and size. If you place one on top of the other, they match exactly. Line segments are congruent if they have the same length.

You can use tick marks to indicate congruent line segments. In the illustration below, line segments AB and BC are congruent.

A C

B

20 m20 m

16 m

Course 2

8-1 Building Blocks of Geometry

Identify the line segments that are congruent in the figure.

Additional Example 3: Identifying Congruent Line Segments

A B

DC

E FAB CD

AC BD

BF DF EC AE

One tick mark

Two tick marks

Three tick marks

The symbol means “is congruent to.”

Reading Math

Course 2

8-1 Building Blocks of Geometry

Check It Out: Example 3

Identify the line segments that are congruent in the figure.

Insert Lesson Title Here

AB AC

BC DE

BD CE

One tick mark

Two tick marks

Three tick marks

A

B C

D E

Course 2

8-1 Building Blocks of Geometry

You Try

Insert Lesson Title Here

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

Course 2

8-1 Building Blocks of Geometry

AG GD, GB GE

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

Course 2

8-2 Classifying Angles

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 than180°.

A straight angle is an anglethat measures 180°.

Course 2

8-2 Classifying Angles

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

Additional Example 1: Classifying Angles

A. B.

obtuse angle acute angle

Course 2

8-2 Classifying Angles

Course 2

8-2 Classifying Angles

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

Reading Math

A •

B • • C

1

Check It Out: Example 1

Insert Lesson Title Here

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

A. B.

straight angle acute angle

Course 2

8-2 Classifying Angles

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.

Course 2

8-2 Classifying Angles

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

Additional Example 2A: Identifying Complementary and Supplementary Angles

Course 2

8-2 Classifying 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°.

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

Additional Example 2B: Identifying Complementary and Supplementary Angles

Course 2

8-2 Classifying 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

Course 2

8-2 Classifying Angles

PMQ and QMR

O

N

P Q

RM

Since 30° + 75° = 105°, PMQ and QMR are neither complementary or 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

Course 2

8-2 Classifying Angles

BAC and CAF

mBAC = 35° and mCAF = 145°

C

B

D

E

FA

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

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°.

Course 2

8-2 Classifying Angles

mA + mB = 90°

56° + mB = 90°

– 56° – 56°

mB = 34°

Substitute 56° for mA.

Subtract 56° from both sides to isolate mB.

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 complementary, mP + mQ = 180°.

Course 2

8-2 Classifying Angles

mP + mQ = 180°

32° + mQ = 180°

– 32° – 32°

mQ = 148°

Substitute 32° for mP.

Subtract 32° from both sides to isolate mQ.

The measure of Q = 148°.

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

Insert Lesson Title Here

1. straight

obtuse

Course 2

8-2 Classifying Angles

2.

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

Insert Lesson Title Here

3. AZB and BZC neither

Course 2

8-2 Classifying Angles

4. BZC and CZD complementary

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