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1. State the type of angles shown (vertical, supplementary,
complementary). Then find the value of x. Show all work.
Angle
supplementary
Relationship: ________________
10°
x = ________________
1. State the type of angles shown (vertical, supplementary,
complementary). Then find the value of x. Show all work.
Angle
vertical
Relationship: ________________
35°
x = ________________
1. State the type of angles shown (vertical, supplementary,
complementary). Then find the value of x. Show all work.
Angle
complementary
Relationship: ________________
50°
x = ________________
8x – 16 = 4x + 20
x=9
3x + 15 + x + 7 = 94
x = 18
4.Find the value of each angle. Write the number inside the angle.
60°
120°
120°
4.Find the value of each angle. Write the number inside the angle.
90°
90°
50°
4.Find the value of each angle. Write the number inside the angle.
77°
52°
51°
77°
5. Sketch, label, and mark a picture for each description below.
X
A
B
C
D
Y
5. Sketch, label, and mark a picture for each description below.
b. BAC  XAY
B
C
A
X
Y
12un2
14un
4
3
7. Jerry has an idea. Since he knows that an isosceles trapezoid has
reflection symmetry, he reasons, "That means it must have two
pairs of congruent angles." He marks the congruent pairs on his
diagram at right. Similarly mark which angles must be equal due
to reflection symmetry below.
7. Jerry has an idea. Since he knows that an isosceles trapezoid has
reflection symmetry, he reasons, "That means it must have two
pairs of congruent angles." He marks the congruent pairs on his
diagram at right. Similarly mark which angles must be equal due
to reflection symmetry below.
7. Jerry has an idea. Since he knows that an isosceles trapezoid has
reflection symmetry, he reasons, "That means it must have two
pairs of congruent angles." He marks the congruent pairs on his
diagram at right. Similarly mark which angles must be equal due
to reflection symmetry below.
7. Jerry has an idea. Since he knows that an isosceles trapezoid has
reflection symmetry, he reasons, "That means it must have two
pairs of congruent angles." He marks the congruent pairs on his
diagram at right. Similarly mark which angles must be equal due
to reflection symmetry below.
Circle
#1: Has
at least
one
obtuse
angle
G
B C
A
D
F
E
Circle #2:
Has 2 pairs
of sides
equal
Scoring Your Homework
• Count how many problems you missed
or didn’t do
•
•
•
•
•
0-2 missed = 10
3-4 missed = 9
5-6 missed = 8
7-8 missed = 7
9-11 missed = 6
• 12-13 missed = 5
• 14-16 missed = 4
• 17-19 missed = 3
• 20-21 missed = 2
• 22-24 missed = 1
• 25-28 missed = 0
2.3
What’s the Relationship?
Pg. 11
Angles formed by Transversals
2.3 – What's the Relationship?______
Angles Formed by Transversals
In lesson 2.2, you examined vertical
angles and found that vertical angles
are always equal. Today you will look
at another special relationship that
guarantees angles are equal.
2.16 – PARALLEL LINES AND ANGLE
RELATIONSHIPS
Julia wants to learn more about the
angles in parallel lines. An enlarged
view of that section is shown in the
image, with some points and angles
labeled.
a. A line that crosses two or more
other lines is called a transversal. In
Julia's diagram, which line is the
transversal? Which lines are
parallel? (Hint: to name a line use
two letters.)
JK
b. Shade in the interior of x. Then
translate x by sliding the tracing
paper along the transversal until it
lies on top of another angle and
matches it exactly. Which angle in
the diagram corresponds with x.
b
c. What is the relationship
between the measures of x and
b? Must one be greater than the
other, or must they be equal?
Explain how you know.
Congruent, they match up
d. In this diagram x and b are called
corresponding angles because they
are in the same position at two
different intersections of the
transversal (notice they are both the
top right angle). The corresponding
angles in this diagram are equal
because they were formed by
translating a parallelogram. Name all
the other pairs of equal
corresponding angles you can find in
Julia's diagram.
w&a
y&c
z&d
e. Suppose b = 60°. Use what you
know about vertical, supplementary,
and corresponding angle relationships
to find the measures of all the other
angles in Julia's diagram.
120°
a = ______
b=
120°
w = ______
60°
x = ______
60°
60° d = ______
120°
c = ______
60°
y = ______
z =120°
______
120° 60°
60° 120°
120° 60°
60° 120°
2.17 – CORRESPONDING ANGLE
CONNECTIONS
Frank wonders whether
corresponding angles are always
equal. For parts (a) through (d)
below, decide whether you have
enough information to find the
measures of x and y. If you do, find
the angle measures.
135°
135°
53°
???
4x – 25°
4x – 25 = 3x + 10
x = 35
45°
???
135°
45°
???
45°
e. Answer Franks' question: Are
corresponding angles ALWAYS
equal? What must be true for
corresponding angles to be equal?
Lines must be parallel for
corresponding angles to be
congruent
f. Conjectures are often written in the
form, "If...,then...". A statement in ifthen form is called a conditional
statement. Make a conjecture about
correspond angles by completing
this conditional statement:
"If __________________,
lines are parallel then
corresponding angles are
congruent
__________________."
2.18 – OTHER ANGLES FOUND WITH
PARALLEL LINES
Suppose a in the diagram at right
measures 48°. Use what you know
about vertical, corresponding, and
supplementary angle relationships to
find the measure of b.
48°
48°
48°
48°
48°
132°
2.19 – ALTERNATE INTERIOR ANGLES
In problem 2.14, Alex showed that the
shaded angles in the diagram are
congruent. However, these angles also
have a name for their geometric
relationship (their relative positions in
the diagram). These angles are called
alternate interior angles. They are called
"alternate" because they are on opposite
sides of the transversal, and "interior"
because they are both inside parallel
lines.
a. Examine CFG and
BCF. How can you
transform CFG so that
it lands on BCF ?
Translation
and rotation
b. Find another pair of alternate
interior angles in the diagram. Be sure
to use thee letters to name the angles.
EFC
DCF and ______
c. Think about the relationship
between the measures of alternate
interior angles. If the lines are
parallel, are they always congruent?
Are they always supplementary?
Complete the conjecture:
"If lines are parallel, then alternate
interior angles are
_____________________."
congruent
e. Shade in the angles that are
vertical to the alternate interior
angles. What is their relationship?
These angles are called alternate
exterior angles. Why do you think
these angles are called that? What is
the difference between alternate
interior angles and alternate exterior
angles?
Alternate
Exterior angles
Alternate
transversal
and outside
parallel lines
2.20 – SAME-SIDE INTERIOR
ANGLES
The shaded angles in the diagram at
right have another special angle
relationship. They are called sameside interior angles.
a. Why do you think they have this
name?
On same side
of transversal
inside parallel
lines
b. What is the relationship between
the angle measures of same-side
interior angles? Are they always
congruent? Supplementary? Talk
about this with your team, then write
a conjecture about the relationship
of the angle measures.
If lines are parallel, then same-side
interior angles are
___________________.
supplementary
2.21 – ANGLE RELATIONSHIPS
Fill in the table below with a picture
representing each type of angle.
Then complete the angle
relationship statement. Explain why
the angles have the names that they
do. Which angles are congruent
(equal)? Which angles add to 180°?
Corresponding Angles
If lines are parallel, then corresponding angles
congruent
are _____________.
Same-Side Interior Angles
If lines are parallel, then same-side interior
supplementary
angles are _____________________.
Alternate Interior Angles
If lines are parallel, then alternate interior
congruent
angles are _____________________.
Alternate Exterior Angles
If lines are parallel, then alternate exterior
congruent
angles are _____________________.