Transcript Midterm Review Project

Midterm Review Project:
Angle Pairs
BY: [NAME REMOVED]
Angle Pairs: Definitions
Parallel Lines: A pair of lines that never cross
Transversal: A line that crosses a set of parallel
lines
Vertical Angles: A pair of angles that are vertical
to each other, and are congruent
Linear Pair Angles: Two angles that are next to
each other on a line, and are supplementary
B
C
B C
Definitions
Alternate Exterior Angles: Lines that are
opposite of each other, on the outside of
parallel lines, and are congruent
Alternate Interior Angles: Two opposite angles
on the interior of parallel lines, and are
congruent
B
B
C
C
Consecutive Exterior Angles: Two angles, on
one side of a transversal, and on the inside
of two parallel lines
B
C
Corresponding Angles: The angles in matching
corners of where the transversal intersects two
parallel lines
B
C
Postulates and Theorems
Linear Pairs Postulate- A linear pair will always add to 180 degrees
Vertical Pairs Postulate- Vertical pairs are always congruent
Corresponding Angles Theorem- Corresponding angles are always congruent
Alternate Exterior Angles Theorem- Alternate exterior angles are always congruent
Alternate Interior Angles Theorem- Alternate interior angles are always congruent
Consecutive Interior Angles Theorem- A pair of consecutive interior angles will always be
supplementary
Tips and Tricks
While working on these problems, remember that if it’s too hard for you to remember all these
theorems and postulates, then just try to remember these three: the vertical angles postulate,
linear pairs postulate, and the alternate interior angles theorem. For any angles pair problem
you can use these three to find the answer. For example, in the problem below you want to know
the measure of angle A. You know that C=36 because of the Vertical Pairs postulate. Then, you
know that C=B because of the Alternate Interior Angles theorem, and finally, you know that
A=144 because you know that B=36 so, because of the Linear Pairs Postulate, 180-36=144.
A
Use your toolbox!!
B
C
36
And Don’t Forget to Read
the Question!!
Example 1
a
Find the measure of angles a and b.
88 b
92
•Use the vertical angles theorem to find that a=88
•a=88
Vertical Angles Theorem
•b=92
Alternate Interior Angles
Theorem
•Use the Alternate Interior angles theorem to find that
b=92.
Example 2
Find the measure of angles a, b, and c.
93
c
b
102
a
180
-93
87
a=102
b=93
c=87
•Use the Corresponding Angles Theorem to find
that a=102
•Next, use the Corresponding Angles Theorem to
find that b=93
•Finally, use the Linear Pairs Postulate to find that
c=87
Problem #1
Find the measures of angles a and g.
g
68
a
Problem #2
x
Find the measures of angles c and u.
(Think of x as an unknown value)
u
23
c
Problem #3
Find the measures of angles p and b.
p
62-x
X-6
b
Problem #4
Find the value of angles h and e.
h
e
32
65
Problem #5
97
90
42
ℎ2
Find the measures of angles h,
s, and o.
S
B
O
y+47
y-29
Answer Key
Problem 1:
Problem 3:
Problem 5:
a=112
p=151
h=97
g=112
b=29
s=97
o=128
Problem 2:
Problem 4:
c=67
h=57
u=157
e=122