Download PracTest312

Geometry Chapter 3 Practice Problems
1) Let’s prove the Same-Side Interior Angles Theorem. “If two lines cut by a transversal are
parallel, then the pairs of same-side interior angles are supplementary.”
a
Using the diagram, write the Given: and Prove:
2
and complete the proof for the Same-Side
Interior Angles Theorem.
b
3
1
Given:
Prove:
Statement
Justification
_____________________
Given
1 2
_____________________
_____________________

_____________________
L.P.  sum 180
m 2  m 3  180
_____________________
_____________________
_____________________
t
's  m
2) Use the given information to determine which segments must be parallel. If there are no such
segments, write none. (Parts a), b), c), d), e) are independent from each other.)
a)
7 4
b)
4 1
c)
6 3
d)
8 5
e) m 7  m 3  m 2  180
3) Convince me that
m.
4) Assume none of the angles are right angles.
(It might help to “pretend” one angle is something like 20 and go from there.)
Put a circle around the statements that are true only if m n.
Put a box around the statements that are true regardless of whether or not m n.
Put an X through the statements that must be false if m n.
1 5
m 2  m 4  180
5 8
m 3  m 5  180
2 7
3 6
m
1
2
3
m 3  m 7  180
5
n
6
7
4 6
8
p
(Every one of these statements will have one thing done to it.)
5) Line m has the equation: y 
4
1
x  13, 417.2321
2
a) Write the equation of the line parallel to line m that passes through (6, -1).
b) Write the equation of the line perpendicular to line m that passes through (6, -1).
6) Line a passes through the points (5, 8) and (7, 14). Line b is given by the equation y  2 x  3.
Are the two lines parallel? Show your work and explain your answer.
7) Each interior angle of a regular n-gon measures 140 . How many sides does the polygon
have?
8) Circle the figures that give enough information to prove that
a)
1 is a right angle.
b)
1
2
1
1 2
c)
d)
1
90
3
2
2
1
3, m 3  45
9) Complete the following proof.
a
5
2 and 3 are supplementary
1 5
Given:
4
b
3
Prove: a b
2
Statements
(1)
2 and
Justifications
3 are supp
c
1
_____________________
m
(2)
b c
_____________________
(3)
1 5
_____________________
(4)
a c
_____________________
(5)
a b
_____________________
10) Refer to the figure. Show your work.
a) Given:
m8  91
m2  50
Find:
m7
b) Given:
Find:
c) Given:
m4  94
m11  55
m2
m2  8x  72 
m5   x 2  40  
Find:
m6   20  6 x  
x
1
2
4 5
8 9
3
6
7
10 11
11) Write a flow proof.
Given: a b, b c,
Prove:
1 4
a
b
1
2
c
m
3
(Hint: It is unnecessary to show a c. )
m
12) A triangle has vertices A(6, 7), B(12, 10) and C(1, 17).
Convince me that triangle ABC is or is not a right triangle.
Bonus: Classify the triangle according to its side lengths.
4