Download 1) Consider the conditional statement: “If a figure is a rectangle, then

Exam 1 – MATH 083 – Geometry
1) Consider the conditional statement: “If a figure is a rectangle, then it is a quadrilateral.”
a) Write which part is the hypothesis and which is the conclusion.
Hypothesis:
Conclusion:
b) Write the converse, the inverse, and the contrapositive of the conditional statement.
Converse:
Inverse:
Contrapositive:
2) Make a CONCLUSION to the given argument; if the argument is INVALID, state your finding.
a) If someone wants to be a successful student, then they must work hard.
Amanda is a successful student at the College of the Canyons.
b) If a quadrilateral is an isosceles trapezoid, then it diagonals are congruent.
Quadrilateral ABCD has congruent diagonals.
c) If a triangle is a right triangle, then it cannot have an obtuse angle.
In triangle VABC , the measure of angle B is 135 .
Exam 1 – MATH 083 – Geometry
3) For full credit, show all your work.
Given: a line segment AB with A  Q  B
AB  x2  10 x  4
AQ  3x  2
BQ  x2  4 x  7
Find: x , AQ , QB and AB .
Exam 1 – MATH 083 – Geometry
4) Fill in the missing statements and reasons for the proof.
Given: 1 is supp. to 2
3 is supp. to 2
Prove: 1  3
Statements
PROOF
Reasons
1.
1.
2.
2. Measures of suppl. angles add up to 180°
3. m1  m2  m3  m2
3.
4.
4. Subtraction
5.
5.
5) Consider the relation “is perpendicular to.” Does it have a reflexive, symmetric, or transitive property?
Justify your reasoning.
Exam 1 – MATH 083 – Geometry
6) With a compass and a ruler, carry out the following constructions (as shown in class).
a) Given: Line
l
containing point A
Construct: 135 angle with vertex at A .
b) Given: Point P not on the line
l
Construct: Line k through the point P so that
k Pl .
Exam 1 – MATH 083 – Geometry
7) Based on the information provided, which lines are parallel? Explain why.
If the information is insufficient, state your finding.
a) 1  2
b) 1  3
c) 1 supp. to 4
d) 4 supp. to 5
e) 5 supp. to 6
f) 6  9
g) 2  8
h) 5  8
i) 7 supp. to 10
j) 9  10
Exam 1 – MATH 083 – Geometry
8) Given:
Lines m P n with a transversal t
m1  2 x  y  20
m2  x  2 y  50
m3  y  100
Find:
x , y , m1 , m2 , and m3
Exam 1 – MATH 083 – Geometry
9) Given: Regular octagon ABCDEFGH with a diagonal AC
Exterior angle 3
Prove: m1  m2  m3
Hint: extend a side at vertex B to form an exterior angle 4 .
Statements
PROOF
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
10) Use indirect proof.
Given: ABD  DBC
uuur
Prove: BD does not bisect ABC
Exam 1 – MATH 083 – Geometry
11) Consider the pentagon ABCDE with two right angles at vertices A and E .
a) The diagonal BD separates the pentagon into a triangle BCD and a quadrilateral ABDE .
Given:
1  2
Find:
m1 , m2 , and m3
b) Find the measures of interior angles: mA , mB , mC , mD and mE . What is their sum?
c) Find the measures of exterior angles: E A , EB , EC , ED , and EE . What is their sum?
d) Verify the formula for the sum S I of measures of interior angles of a pentagon.
e) Verify the value for the sum S E of measures of exterior angles of a pentagon.