Name: ______________________________________________
Geometry
Problem Set #5
Show all work for full credit.
1) Which Venn diagram accurately represents the
information in the following statement?
If a triangle is equilateral, then it is isosceles.
Answer = ___________________
3) Given S(-1, 8) and T(7, -10). What is ST? (hint: when
there is no symbol over two points, it means what?)
Block : _____________Date Due______________
2) What is the slope of the line that is perpendicular to the
given one in the picture?
Slope of the line Perpendicular = _________________
4) Given Statements:
If a shape is a parallogram, then opposite angles are
congruent. A rhombus is a parallelogram.
Which is a logical conclusion from the given statements?
a) A rhombus has opposite angles that are congruent.
b) The opposite sides of a rhombus are congruent.
c) The diagonals of a rhombus are congrent.
d) A rhombus is a quadrilateral.
Answer = ________________
ST = ___________
5) Which is the converse of the following statement?
a
If  c, then a  bc
b
a
a) if  c, then a  bc
b
a
b) if a  bc, then  c
b
a
c) if a  bc, then  c
b
a
d) if  c, then a  bc
b
Answer = ________________
6) Let p represent, “Brent works this summer”, and let q
represent “Brent takes a vacation.”
Symbolically represent the following argument:
Symbolic answer
If Brent works this summer,
then he will not take a vacation.
________________
Brent takes a vacation.
________________
Therefore, Brent does not
work this summer.
________________
7) Let p represent, “Two angles are vertical angles” and
let q represent, “the angles are congruent.” If the
conditional is written as pq, write the contrapositive
and give the symbolic notation.
8) The given diagram represents the students who play in
the orchestra. Shade the region(s) that show students
who play only the flute AND the Oboe.
Statement: ____________________________________
______________________________________________
Symbolic notation: ___________________________
9) Which is a valid conclusion that can be drawn from
these statements? If a quadrilateral is a rhombus, then
it is a parallelogram. If a quadrilateral is a
parallelogram, then its opposite angles are congruent.
10) Write the inverse and its symbolic notation of the
following statement?
If the measure of an angle is 90o, then it is a right angle.
Inverse: ______________________________________
Conclusion: __________________________________
_____________________________________________
______________________________________________
_____________________________________________
______________________________________________
Symbolic Notation: _____________________________
11) Given the following graph and the line: x  2 y  5 ,
What is the relationship between the equation of the
line given and the graphed line below?
12) Solve the triangle for the value of y.
y 8
Relationship:________________________
13) What is the slope of the line that goes through the
following two points: P (5, -7) and S (-3, 3)?
m = ________________________
y = _____________
14) Shade the region that shows when a rectangle can be
a rhombus.