Geometry Chapter 2 Study Guide
Chapter 2 Vocab:
Theorem
Conclusion
Reflexive
Hypothesis
Symmetric
Converse
Deductive reasoning
Transitive
Biconditional
Truth value
1.
Find a counterexample:
 If it is not a weekday, then it is a Saturday. Sunday
 If you live in a country that borders the United States, then you live in Canada. Mexico
2.
Write the converse:
 If you eat your vegetables, then you grow. If you grow, then you eat your vegetables.
 If two segments are congruent, then they have the same length. If two segments have the
same length, then they are congruent.
3.
Write the converse of the statement, then determine the truth value of the conditional and
the converse:
 If you travel from the United States to Kenya, then you have a passport. true, If you have
a passport, then you travel from the US to Kenya, false
 If a point is in the first quadrant, then its coordinates are positive. true, If a point’s
coordinates are positive, then it is in the first quadrant, true
4.
Write the two statements that form the biconditional:
 A line bisects a segment if and only if the line intersects the segment only at its midpoint.
If a line bisects a segment, then it intersects the segment only at its midpoint. If a line
intersects a segment only at its midpoint, then it bisects the segment.
 Two angles are congruent if and only if they have the same measure. If two angles are
congruent, then they have the same measure. If two angles have the same measure, then
they are congruent.
5.
If the conditional is reversible, write the biconditional:
 A Tarheel is a person who was born in North Carolina. not reversible
 A midpoint of a segment is a point that divides a segment into two congruent segments.
A point is a midpoint if and only if it divides a segment into two congruent segments.
6.
Use the Law of Detachment and the Law of Syllogism to make a conclusion:
 If you live in Lubbock, then you live in Texas. Levon lives in Lubbock. If you live in
Texas, then you live in the 28th state to enter the Union. Levon lives in the 28th state to
enter the Union.
 If games are canceled, then Maria reads a book. If it snows, then games are canceled. It
is snowing. Maria is reading a book.
7.
Fill in the reason to justify each step:
3(n+4)
3n
X
Z
Given: XY = 42
XZ + ZY = XY
3(n + 4) + 3n = 42
3n + 12 + 3n = 42
6n + 12 = 42
6n = 30
n=5
8.
Y
a.___________________
b.___________________
c.___________________
d.___________________
e.___________________
f.____________________
Find the value of each variable and the measure of each angle:
P
N
(3x+8)
M
(5x-20)
(5x+4y)
Q
O
9.
Find the value of each variable and the measure of each angle:
U
S
4y
2x
R
(x+y+10)
T
V