1. Building Blocks of Geometry
Course 2
8-1
Building Blocks of Geometry
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 or rectangle
point
Hwk p 68 & 69 THIS SHOULD BE A REVIEW

2. Building Blocks of Geometry
Course 2
8-1
Building Blocks of Geometry
EQ: How do I identify / describe the building blocks of geometry and identify angles?
M7P1.a Build new mathematical knowledge through problem solving;
M7P1.b Solve problems that arise in
mathematics and in other contexts;

3. Review %

4. Building Blocks of Geometry
Course 2
8-1
Building Blocks of Geometry
A point is an exact
location in space. It is usually represented as a dot, but it has no size at all
• A
point A
Use a capital
letter to name
a point.
A line is a straight path that extends without end in opposite directions.
XY, or YX
Use two points
on the line to
name a line. X Y
A number line is an example of a line.
Helpful Hint

5. Building Blocks of Geometry
Course 2
8-1
Building Blocks of Geometry
A plane is a
perfectly flat
surface that
extends infinitely
in all directions.
plane QRS
Use three points
in any order, not
on the same line,
to name a plane. Q R S
A coordinate plane is an example of a plane.
Helpful Hint

6. Additional Example 1: Identifying Points, Lines, and Planes
Course 2
8-1
Building Blocks of Geometry
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

7. Insert Lesson Title Here
Course 2
8-1
Building Blocks of Geometry
Insert Lesson Title Here
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

8. Building Blocks of Geometry
Course 2
8-1
Building Blocks of Geometry
A ray is a part of a line.
It has one endpoint and
extends without end in
one direction. GH
Name the endpoint
first when naming
a ray. H G
A line segment is
part of a line. or a ray
that extends from one
endpoint to another.
LM, or ML
Use the endpoints
to name a line
segment. L M

9. Additional Example 2: Identifying Line Segments and Rays
Course 2
8-1
Building Blocks of Geometry
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

10. Building Blocks of Geometry
Course 2
8-1
Building Blocks of Geometry
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
BA, CA, BD
Use the endpoints in any order to name a segment.

11. Building Blocks of Geometry
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. B
20 m
20 m A C
16 m

12. Additional Example 3: Identifying Congruent Line Segments
Course 2
8-1
Building Blocks of Geometry
Additional Example 3: Identifying Congruent Line Segments
Identify the line segments that are congruent in the figure. A B D C E F
AB CD
One tick mark
AC BD
Two tick marks
BF DF EC AE
Three tick marks
The symbol means “is congruent to.”
Reading Math

13. Insert Lesson Title Here
Course 2
8-1
Building Blocks of Geometry
Insert Lesson Title Here
Check It Out: Example 3
Identify the line segments that are congruent in the figure. A B C D E
AB AC
One tick mark
BC DE
Two tick marks
BD CE
Three tick marks

14. Building Blocks of Geometry Insert Lesson Title Here
Course 2
8-1
Building Blocks of Geometry
Insert Lesson Title Here
You Try
Identify the figures in the diagram.
1. lines
AD, BE, CF
2. plane
Possible 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.
AG GD, GB GE

15. Course 2
8-2
Classifying Angles A C B 1
Vertex
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 (°).

16. 8-2 Classifying Angles An angle’s measure determines the type of
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°. The
symbol indicates a right angle.
An acute angle is an angle
that measures less than 90°.
An obtuse angle is an angle
that measures more than 90°
but less than180°.
A straight angle is an angle
that measures 180°.

17. Additional Example 1: Classifying Angles
Course 2
8-2
Classifying Angles
Additional Example 1: Classifying Angles
Tell whether each angle is acute, right, obtuse or straight. A. B.
obtuse angle
acute angle

18. 8-2 Classifying Angles Reading Math
Course 2
8-2
Classifying Angles
You can name this angle ABC, CBA, B, or 1.
Reading Math
A •
B •
• C 1

19. Insert Lesson Title Here
Course 2
8-2
Classifying Angles
Insert Lesson Title Here
Check It Out: Example 1
Tell whether each angle is acute, right, obtuse, or straight. B. A.
straight angle
acute angle

20. 8-2 Classifying Angles If the sum of the measures of two angles is
Course 2
8-2
Classifying Angles
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.

21. Course 2
8-2
Classifying Angles
Additional Example 2A: Identifying Complementary and Supplementary Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
OMP and PMQ
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°. O N P Q R M
Since 60° + 30° = 90°, PMQ and OMP are complementary.

22. Course 2
8-2
Classifying Angles
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. O N P Q R M
Read mNMO as “the measure of angle NMO.”
Reading Math

23. Course 2
8-2
Classifying Angles
Additional Example 2C: Identifying Complementary and Supplementary Angles
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
PMQ and QMR
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°. O N P Q R M
Since 30° + 75° = 105°, PMQ and QMR are neither complementary or supplementary.

24. 8-2 Classifying Angles Check It Out: Example 2A
Course 2
8-2
Classifying Angles
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. C B D E F A

25. Additional Example 3: Finding Angle Measures
Course 2
8-2
Classifying Angles
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.
– 56° – 56°
Subtract 56° from both sides to isolate mB.
mB = 34°
The measure of B = 34°.

26. 8-2 Classifying Angles Check It Out: Example 3
Course 2
8-2
Classifying Angles
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 complementary, mP + mQ = 180°.
mP + mQ = 180°
32° + mQ = 180°
Substitute 32° for mP.
– 32° – 32°
Subtract 32° from both sides to isolate mQ.
mQ = 148°
The measure of Q = 148°.

27. Insert Lesson Title Here
Course 2
8-2
Classifying Angles
Insert Lesson Title Here
TOTD
Tell whether each angle is acute, right, obtuse, or straight. 1.
straight 2.
obtuse

28. Insert Lesson Title Here
Course 2
8-2
Classifying Angles
Insert Lesson Title Here
TOTD
Use 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 M is 117°, what is mN?
63°