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Transcript
```Introduction to Geometry: Points, Lines, and Planes
PRE-ALGEBRA LESSON 9-1
Quick Check
Use the figure to name each of the following.
a. four points
H, I, J, and K
Name a point with a capital letter.
b. four different segments
HO, HJ , KI, and OI
Name a segment by its endpoints.
c. five other names for KI
IK , KO, OK , IO , and OI
Horizontal line KI has several names.
d. five different rays
HO, OJ, KI , OK , and JH
The first letter names the endpoint.
9-1
Introduction to Geometry: Points, Lines, and Planes
PRE-ALGEBRA LESSON 9-1
You are looking directly down into a wooden crate. Name
each of the following.
a. four segments that intersect PT
MP, OP, QT, ST
b. three segments parallel to PT
MQ, NR, OS
c. four segments skew to PT
MN, NO, QR, RS
Quick Check
9-1
Introduction to Geometry: Points, Lines, and Planes
PRE-ALGEBRA LESSON 9-1
Draw two intersecting lines. Then draw a segment that is
parallel to one of the intersecting lines.
Use the lines on notebook or graph paper.
First draw two lines that intersect.
Then draw a segment that is parallel to one of
the lines.
Quick Check
9-1
Introduction to Geometry: Points, Lines, and Planes
PRE-ALGEBRA LESSON 9-1
Use the figure. Name each of the following.
1. four points A, B, C, D
2. another name for EA
3. three different rays
EQ
AQ, AE, GR
4. three segments that are parallel to HG
5. four segments that are skew to CG
6. four segments that intersect AE
9-1
EF, DC, AB
Angle Relationships and Parallel Lines
PRE-ALGEBRA LESSON 9-2
The Jackson County Bird Sanctuary has three times as many owls as
hawks. It has 40 hawks and owls in all. How many of each are in the
sanctuary?
30 owls, 10 hawks
9-2
Angle Relationships and Parallel Lines
PRE-ALGEBRA LESSON 9-2
(For help, go to Lesson 7-5.)
Solve.
1. n + 45 = 180
2. 75 + x = 90
3. 3y = 2y + 90
4. 2a + 15 = a + 45
Check Skills You’ll Need
9-2
Angle Relationships and Parallel Lines
PRE-ALGEBRA LESSON 9-2
Solutions
1.
n + 45 = 180
n + 45 – 45 = 180 – 45
n = 135
2.
75 + x = 90
75 – 75 + x = 90 – 75
x = 15
3.
3y = 2y + 90
3y – 2y = 2y – 2y + 90
y = 90
4.
2a + 15 = a + 45
2a – a + 15 = a – a + 45
a + 15 = 45
a + 15 – 15 = 45 – 15
a = 30
9-2
Angle Relationships and Parallel Lines
PRE-ALGEBRA LESSON 9-2
Find the measure of
m
m
m
3+m
3 if m
4 = 180°
4 = 110°.
3 and
4 are supplementary.
3 + 110° = 180°
Replace m
4 with 110°.
3 + 110° – 110° = 180° – 110°
Solve for m
3.
m
3 = 70°
Quick Check
9-2
Angle Relationships and Parallel Lines
PRE-ALGEBRA LESSON 9-2
In the diagram, p || q. Identify each of the following.
a. congruent corresponding angles
1
3,
2
4,
5
7,
6
8
b. congruent alternate interior angles
2
7,
6
3
Quick Check
9-2
Angle Relationships and Parallel Lines
PRE-ALGEBRA LESSON 9-2
In the diagram, d e.
1. Find the m 5 if m 8 is 35°.
145°
2. Name the congruent corresponding angles.
1
5,
2
6,
4
8,
3
7
3. Name the congruent alternate interior angles.
4
7,
2
5
9-2
```