parallel and perpendicular lines - kyrene school …...course 2 7-3 parallel and perpendicular lines...
TRANSCRIPT
Learn to identify parallel, perpendicular, and skew lines, and angles formed by a
transversal.
Course 2
7-3 Parallel and Perpendicular Lines
Vocabulary
perpendicular lines
parallel lines
intersecting lines
skew lines
vertical angles
complimentary angles
supplementary angles
transversal
Insert Lesson Title Here
Course 2
7-3 Parallel and Perpendicular Lines
Course 1
7-3 Angle Relationships
65° + 25° = 90°
LMN and NMP are complementary.
Complementary angles are two angles whose measures have a sum of 90°.
P
N
M
L
25° 65°
Course 1
7-3 Angle Relationships
Supplementary angles are two angles whose measures have a sum of 180°.
65° + 115° = 180°
GHK and KHJ are supplementary.
J
K
H
115° 65°
G
Course 2
7-3 Parallel and Perpendicular Lines
When lines, segments, or rays intersect, they form angles. If the angles formed by two intersecting lines are equal to 90°, the lines are perpendicular lines.
Line RS is perpendicular to line TU.
RS TU. S
R
T U
The square inside a right angle shows that the rays of the angle are perpendicular.
Writing Math
Course 2
7-3 Parallel and Perpendicular Lines
Some lines in the same plane do not intersect at all. These lines are parallel lines. Segments and rays that are part of parallel lines are also parallel.
Line AB is parallel to line ML.
AB ML.
B
A
M
L
Course 2
7-3 Parallel and Perpendicular Lines
Skew lines do not intersect, and yet they are also not parallel. They lie in different planes.
Line AB and line ML are skew.
AB and ML are skew.
M
L
A B
Course 2
7-3 Parallel and Perpendicular Lines
Intersecting Lines lines that cross at one common point.
Line YZ intersects line WX.
YZ intersects WX.
Y W
Z X
Course 2
7-3 Parallel and Perpendicular Lines
The symbol means “is parallel to.” The symbol means “is perpendicular to.”
Reading Math
Tell whether the lines appear parallel, perpendicular, or skew.
Additional Example 1A: Identifying Parallel,
Perpendicular, and Skew Lines
Course 2
7-3 Parallel and Perpendicular Lines
A. UV and YV The lines appear to intersect to form right angles. UV YV
X Y
V
Z W
U
Tell whether the lines appear parallel, perpendicular, or skew.
Additional Example 1B: Identifying Parallel,
Perpendicular, and Skew Lines
Course 2
7-3 Parallel and Perpendicular Lines
B. XU and WZ
The lines are in different planes and do not intersect.
XU and WZ are skew.
X Y
V
Z W
U
Tell whether the lines appear parallel, perpendicular, or skew.
Additional Example 1C: Identifying Parallel,
Perpendicular, and Skew Lines
Course 2
7-3 Parallel and Perpendicular Lines
C. XY and WZ
The lines are in the same plane and do not intersect.
XY || WZ
X Y
V
Z W
U
When angles have the same measure, they are said to be congruent.
Vertical angles are formed opposite each other when two lines intersect. Vertical angles have the same measure, so they are always congruent. Kissing angles.
MRP and NRQ are vertical angles.
MRN and PRQ are vertical angles
M N 160°
160°
20° 20° R
P Q
Course 2
7-3 Parallel and Perpendicular Lines
Course 1
7-3 Angle Relationships
Adjacent angles are side by side and have a common vertex and ray. Adjacent angles may or may not be congruent.
MRN and NRQ are adjacent angles. They share vertex R and RN.
NRQ and QRP are adjacent angles. They share vertex R and RQ.
M N 160°
160°
20° 20° R
P Q
Course 1
7-3 Angle Relationships
65° + 25° = 90°
LMN and NMP are complementary.
Complementary angles are two angles whose measures have a sum of 90°.
P
N
M
L
25° 65°
Course 1
7-3 Angle Relationships
Supplementary angles are two angles whose measures have a sum of 180°.
65° + 115° = 180°
GHK and KHJ are supplementary.
J
K
H
115° 65°
G
Course 2
7-3 Parallel and Perpendicular Lines
Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.
Reading Math
Course 2
7-3 Parallel and Perpendicular Lines
A transversal is a line that intersects two or more lines.
• Eight angles are formed when a transversal intersects two lines.
• When those two lines are parallel, all of the acute angles formed are congruent, and
• all of the obtuse angles formed are congruent.
• These obtuse and acute angles are supplementary.
1 2
3 4 5 6
7 8
Course 2
7-3 Parallel and Perpendicular Lines
• There are 4 interior angles
• There are 4 exterior angles
1 2
3 4 5 6
7 8
Course 2
7-3 Parallel and Perpendicular Lines
• There are 4 pairs of vertical angles.
• 2 Acute Pairs
• 2 Obtuse Pairs
1 2
3 4 5 6
7 8
Course 2
7-3 Parallel and Perpendicular Lines
• There are 4 pairs of corresponding angles.
1 2
3 4 5 6
7 8
Course 2
7-3 Parallel and Perpendicular Lines
• There are many pairs of adjacent angles… angles that share a ray and are therefore considered to be supplementary angles.
• 2 blues
• 2 reds
• 1 blue & 1 red
1 2
3 4 5 6
7 8
Line n line p. Find the measure of the angle.
Additional Example 2A: Using Angle Relationships to
Find Angle Measures
Course 2
7-3 Parallel and Perpendicular Lines
A. 2
2 and the 130° angle are vertical angles. Since vertical angles are congruent, m 2 = 130°.
Line n line p. Find the measure of the angle.
Additional Example 2B: Using Angle Relationships to
Find Angle Measures
Course 2
7-3 Parallel and Perpendicular Lines
B. 3
3 and the 50° angle are acute angles. Since all of the acute angles in the figure are congruent, m 3 = 50°.
Line n line p. Find the measure of the angle.
Additional Example 2C: Using Angle Relationships to
Find Angle Measures
Course 2
7-3 Parallel and Perpendicular Lines
C. 4
4 is an obtuse angle. Since all of the obtuse angles in the figure are congruent, m 4 = 130°.
Line n line p. Find the measure of the angle.
Try This: Example 2A
Course 2
7-3 Parallel and Perpendicular Lines
A. 3
3 and the 45° angle are vertical angles. Since vertical angles are congruent, m 3 = 45°.
45°
2 3 135° 5 6 4
7
n p
Lesson Quiz
Tell whether the lines appear
parallel, perpendicular, or skew.
1. AB and CD
2. EF and FH
3. AB and CG
4.
perpendicular
parallel
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skew
Both are always the same distance apart, but railroad tracks are not always straight.
Course 2
7-3 Parallel and Perpendicular Lines
How are railroad tracks and two parallel lines alike, and how are they different?
D