1. 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

2. 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

3. Vocabulary
point
line
plane
ray
line segment
congruent

4. l XY, or YX, or l X Y A point is an exact
location. 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. l
A line is a straight path that extends without end in opposite directions.
XY, or YX, or l
Use two points
on the line or a
lowercase letter to
name a line. X Y
Use to complete vocabulary
A number line is an example of a line.
Helpful Hint

5. Has no thickness and extends forever. plane QRS Use three points
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. Q R S
A coordinate plane is an example of a plane.
Helpful Hint

6. 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. Identify the figures in the diagram.
Check It Out: Example 1
Identify the figures in the diagram. G H I F
A. four points
Use as formative assessment; print out worksheet for classwork grade
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. A ray is a part of a line.
It has one endpoint and
extends forever
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
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. Identify the figures in the diagram.
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 as formative assessment; print out worksheet for classwork grade
BA, CA, BD
Use the endpoints in any order to name a segment.

11. Figures are congruent if they have the same shape and size
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.

12. Additional Example 3: Identifying Congruent Line Segments
Identify the line segments that are congruent in the figure.
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. Identify the line segments that are congruent in the figure.
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
Use as formative assessment; print out worksheet for classwork grade

14. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
Print out Lesson Quiz for SRS for quiz on Friday.

15. Lesson Quiz
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

16. Lesson Quiz for Student Response Systems
1. Identify the lines in the diagram. A.
B. AB, AE C. D.

17. 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

18. Lesson Quiz for Student Response Systems
3. Identify three rays in the diagram. A. B. C. D.

19. Lesson Quiz for Student Response Systems
4. Identify the line segments that are congruent in the figure. A. B. C. D.

20. Vocabulary angle vertex right angle acute angle obtuse angle
straight angle
complementary angles
supplementary angles

21. Angles are measured in degrees (°).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 (°).

22. 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 than 180°.
A straight angle is an angle
that measures exactly 180°.

23. Additional Example 1: Classifying Angles
Tell whether each angle is acute, right, obtuse or straight. A. B.
obtuse angle
acute angle

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

25. Tell whether each angle is acute, right, obtuse, or straight.
Check It Out: Example 1
Tell whether each angle is acute, right, obtuse, or straight. B. A.
Use as formative assessment; print out worksheet for classwork grade
straight angle
acute angle

26. 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.

27. 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.

28. 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

29. 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
Use as formative assessment; print out worksheet for classwork grade
Read mNMO as “the measure of angle NMO.”
Reading Math

30. 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
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 nor supplementary.

31. 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

32. Check It Out: Example 2B
Use the diagram to tell whether the angles are complementary, supplementary, or neither.
CAD and EAF
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°. C B D E F A
Since 55° + 35° = 90°, CAD and EAF are complementary.

33. 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. C B D E F A

34. 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.
mB = 34°
The measure of B = 34°.

35. Angles P and Q are supplementary. If mP is 32°, what is the mQ?
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.
Use as formative assessment; print out worksheet for classwork grade
– 32° – 32°
Subtract 32° from both sides..
mQ = 148°
The measure of Q = 148°.

36. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

37. Tell whether each angle is acute, right, obtuse, or straight.
Lesson Quiz: Part I
Tell whether each angle is acute, right, obtuse, or straight. 1.
straight 2.
Print out Lesson Quiz for SRS for quiz on Friday.
obtuse

38. Lesson Quiz: Part II
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M is 117°, what is mN?
63°

39. Lesson Quiz for Student Response Systems
1. Identify the type of the given angle.
A. acute
B. obtuse
C. right
D. straight

40. Lesson Quiz for Student Response Systems
2. Identify the type of the given angle.
A. acute
B. obtuse
C. right
D. straight

41. 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

42. 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°