Download Parallel Lines Cut by Transversal Lesson PP

Vocabulary Review
&
Special Angles Created When
Parallel Lines are Cut by a
Transversal
with Ms. Evans & Ms. Straka
Parallel Lines Cut by a Transversal – Part A
https://www.youtube.com/watch?v=w6PVwdJXhdk
Parallel Lines Cut by a Transversal – Part B
https://www.youtube.com/watch?v=Cl81BvbjRMg
Parallel Lines Cut by a Transversal - Part A & B
https://www.youtube.com/watch?v=LxIiUUJrsrY
Vocabulary Review
Angle Review
An angle () is formed by two rays with a
common endpoint called the vertex (plural,
vertices). Angles can be measured in degrees.
1
One degree, or 1°, is
of a circle.
360
m1 means the “measure of 1”.
An angle can be named XYZ, ZYX, 1, or Y.
The vertex must be the middle letter.
X
Y
1
Z
m1 = 50°
The measures of angles that fit together to form
a straight line, such as FKG, GKH, and
HKJ, add to 180°.
G
F
H
K
J
The measures of angles that fit together to form
a complete circle, such as MRN, NRP, PRQ,
and QRM, add to 360°.
P
N
M
R
Q
Acute Angles – measure less than 90 degrees.
• <FKG is acute.
Obtuse Angles – measure more than 90
degrees.
• <GKJ is obtuse.
G
F
H
K
J
A right angle measures 90°.
Reading Math
A right angle can be labeled with a small box at
the vertex.
1st & 2nd Tabs in
Vocab Flip Book
The notes that follow match the guided notes provided in the
Parallel Lines Cut by a Transversal Vocabulary Flip Book, which
was given in class.
• Fill in the blanks.
EX: Right angles measure 90 degrees.
• Draw a picture in the block on the left or
right of the notes.
• We will complete the folding, cutting, and
gluing of the Vocabulary Flip Book
in class.
Complementary angles: Angles whose
measures sum to 90°. A right angle measures
90°.
Angle symbol
∡
Supplementary angles: Angles whose
measures sum to 180°. A straight line measures
180°.
Example: Classifying Angles
A. Name a pair of complementary angles.
TQP, RQS mTQP + m RQS = 47° + 43° = 90°
Example: Classifying Angles
B. Name two pairs of supplementary angles.
TQP, RQT mTQP + m RQT = 47° + 133° = 180°
3rd Tab in Vocab Flip Book
Vertical Angles: Angles formed by 2 intersecting
lines. Vertical angles are always congruent.
Congruent Symbol:
≅
In the figure, 1 and 3 are vertical
angles, and 2 and 4 are vertical angles.
Example: Finding the Measure of Vertical Angles
In the figure, 1 and 3 are vertical
angles, and 2 and 4 are vertical angles.
If m1 = 37°, find m 3.
1 and 3 are vertical angles.
m3 = 37°
4th Tab in Vocab Flip Book
Parallel lines are lines in a plane that
never meet, like a set of perfectly
straight, infinite train tracks.
The symbol for parallel is ||.
The railroad ties are transversals to the tracks.
The
tracks
are
parallel.
A transversal is a line that intersects 2 or more
lines in the same plane.
It creates angles with special properties when it
intersects parallel lines.
Example: Identifying Congruent Angles Formed
by a Transversal
Look at the angles formed by the
transversal and parallel lines. Which
angles seem to be congruent?
1, 3, 5, and 7 all measure 150°.
 2, 4, 6, and 8 all measure 30°.
Example Continued
Angles marked in blue appear to be
congruent to each other, and angles marked
in red appear to be congruent to each other.
1 @ 3 @ 5 @ 7
2 @ 4 @ 6 @ 8
2
1
3 4
6 5
7 8
5th Tab in Vocab Flip Book
Perpendicular lines: Lines that intersect
at 90° angles.
The symbol for perpendicular is .
Coincidental Lines are the same line.
6th Tab in Vocab Flip Book
Alternate interior angles: 2 angles
on opposite sides of the transversal and
inside the parallel lines. These angles are
≌.
The pair of blue and the pair of pink angles are
alternate interior angles.
7th Tab in Vocab Flip Book
Alternate exterior angles: 2 angles
on opposite sides of the transversal and
outside the parallel lines. These angles
are ≌.
The pair of blue and the pair of pink angles are
alternate exterior angles.
8th Tab in Vocab Flip Book
Corresponding angles: Angles in
matching corners when 2 parallel lines are
crossed by a transversal. Corresponding
angles are ≌.
The pair of pink angles are corresponding. The
pair of purple angles are corresponding. The
blue pairs and green pairs are also
corresponding.
Other Angles
Same side interior or consecutive
interior angles are 2 angles inside the 2
parallel lines along the same side of a
transversal line. These angles are
supplementary.
1
2
3 4
5 6
7 8
Ex: <3 and <5 are same side interior angles.
<4 and <6 are same side interior angles.
Same side exterior or consecutive
exterior angles are 2 angles outside the
2 parallel lines along the same side of a
transversal line. These angles are
supplementary.
1
2
3 4
5 6
7 8
Ex: <1 and <7 are same side exterior angles.
<2 and <8 are same side exterior angles.
Properties of 2 Parallel
Lines Cut by a
Transversal
Add the notes below to your MSG.
PROPERTIES OF TRANSVERSALS
TO PARALLEL LINES
If two parallel lines are intersected by a transversal,
• the acute angles that are formed are all congruent,
• the obtuse angles are all congruent,
• and any acute angle is supplementary to any
obtuse angle.
If the transversal is perpendicular to the parallel
lines, all angles are 90°.
Example: Finding Angle Measures of Parallel
Lines Cut by Transversals
In the figure, line l (L) || line m. Find the
measure of the angle 4.
All obtuse angles in the figure are congruent.
m4 = 124°
Example: Finding Angle Measures of Parallel
Lines Cut by Transversals Continued
In the figure, line l || line m. Find the
measure of the angle 2.
2 is supplementary to the angle 124°.
m2 + 124° = 180°
–124° –124°
m2
= 56°