Download Paper Pre-Assessment: Reasoning Multiple

Reasoning Pre-Assessment
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Determine the next number in the sequence below. Is this inductive or deductive reasoning?
1, 2, 4, 7, 11...
____
A. The next number is 22. This is
inductive reasoning.
C. The next number is 16. This is
inductive reasoning.
B. The next number is 22. This is
deductive reasoning.
D. The next number is 16. This is
deductive reasoning.
2. Use deductive reasoning to make a correct conclusion. If you are in 10th grade, then you are taking
Geometry. You are in 10th grade.
____
____
A. You are taking Geometry.
C. It cannot be determined if you are
taking Geometry.
B. You are not taking Geometry.
D. You are a sophomore.
3. Which of the following statements represents logical reasoning?
A. an algebraic equation
C. an observed experiment
B. a doctor examining a patient
D. a geometric proof
4. One axiom or postulate of Euclidean Geometry is:
A. Vertical angles are congruent.
B. A parrallelogram has two pair of
parallel sides.
____
C. Parallel lines always have
corresponding angles.
D. A straight line can be drawn to connect
any two points.
5. What are the undefined terms of Geometry?
A. Point and line
C. Point and plane
B. Point, line and plane
D. Point, line and circle
____
6. Determine which conjuction below is true.
A. An isosceles triangle has two
congruent sides and congruent base
angles.
C. A scalene triangle has three noncongruent sides and three acute angles.
B. An equilateral triangle has three
D. An isosceles triangle has two
congruent sides and three 120º angles.
congruent sides and three acute angles.
____
7. Use the statement below to determine which condition makes the disjunction false.
“A quadrilateral is a parallelogram or a trapezoid”
____
____
A. A square is a quadrilateral.
C. A kite is a quadrilateral.
B. A rectangle is a parallelogram.
D. A trapezoid is not a parallelogram.
8. Determine which existential statement is correct.
A. There exists an x, such that -x is a
positive number.
C. For all x,
B. There exists an x, such that
positive number.
D. For all x,
is a
is a negative number.
is a negative number.
9. Write a conditional statement based on the declarative:
“A rhombus is a parallelogram with four equal sides.”
A. If a parallelogram has right equal
sides, then it is a rhombus.
C. If a parallelogram is a rhombus, then it
has four equal sides.
B. If a rhombus has four equal sides, then D. If a rhombus is a parallelogram, then it
it is a parallelogram.
has four equal sides.
____ 10. Which part of the statement below is the hypothesis?
“If a triangle has one right angle, then it is a right triangle.”
A. A triangle is a right triangle.
C. A right triangle has one right angle.
B. A triangle has one right angle.
D. A right triangle has two acute angles.
____ 11. What statement would you begin with if you were going to prove that alternate interior angles,
and
, have the same measure using a proof by contradiction?
A.
and
angles.
are not alternate interior
C.
B.
and
angles.
are same-side interior
D.
____ 12. When do you know you have completed a proof by contradiction?
A. When there are two statements in your C. When you have used the same reason
proof that are exact opposites.
more than once.
B. When there are two statements in your D. When you write QED.
proof that are exactly the same.
____ 13. Determine which statement below is true.
A. Sunlight is a necessary condition for
growing food.
C. Studying for a test is a necesary
condition for passing the test.
B. Getting all A’s in high school is a
necessary condition for getting into
college.
D. Rain is a necessary condition to make
the ground wet.
____ 14. Determine which statement below is true.
A. Having two pair of congruent sides is a C. Having four congruent sides is a
sufficient condition to make a
sufficient condition to make a
quadrilateral a kite.
parallelogram a square.
B. Being female is a sufficient condition
to being a mother.
D. Having two congruent sides is a
sufficient condition to make a triangle
isosceles.
____ 15. Determine which statement below is true.
A. A parallelogram with four congruent
C. A triangle with three acute angles is
sides is necessary and sufficient to say
necessary and sufficient to say the
the figure is a square.
triangle is equiangular.
B. A rectangle with four congruent sides
is necessary and sufficient to say the
figure is a square.
D. Two angles whose measures add up to
180º is necessary and sufficient to say
the two angles form a linear pair.
Use the figure and proof below for the next two questions.
Given: n and m are parallel
Prove:
and
are congruent.
Statements
1. n and m are parallel
2.
3.
4.
Reasons
1. Given
2. Reason A
3. parallel lines imply
corresponding angles are
congruent
4. Reason B
____ 16. Determine the correct reason to put in the “Reason A” spot in the proof above.
A. parallel lines imply alternate interior
C. vertical angles are congruent
angles are congruent
B. parallel lines imply that corresponding D. parallel lines imply alternate exterior
angles are congruent
angles are congruent
____ 17. Determine the correct reason to put in spot “Reason B” in the proof above.
A. substitution property of equality
C. transitive property
B. parallel lines imply alternate exterior
angles are congruent
D. reflexive property
Use the figure and proof below for the next two questions.
Given: n and m are parallel
Prove:
and
are supplementary
Statements
1. line m and line n are
parallel
2.
3.
4.
5.
6.
and
are
supplementary
Reasons
1. Given
2. Reason A
3. parallel lines imply
corresponding angles are
congruent
4. Congruent angles have
the same measure.
5. Reason B
6. Definition of
supplementary angles.
____ 18. Determine the correct reason for “Reason A” in the proof above.
A. a linear pair has a sum of 180º
B. supplementary angles have a sum of
180º
C. complementary angles have a sum of
180º
D. corresponding angles have a sum of
180º
____ 19. Determine the correct reason for “Reason B” in the proof above.
A. transitive property
C. reflexive property
B. addition property of equality
D. substitution property of equality
Use the figure and proof below for the next three questions.
Given:
and
Prove:
1.
2.
3.
4.
Statements
and
1.
2.
3.
4.
Reasons
Given
Reason A
Reason B
Reason C
____ 20. Determine the correct reason for “Reason A” in the proof above.
A.
and
are corresponding
angles
B.
C.
and
are supplementary
angles
and
are complementary
D. vertical angles are congruent
angles
____ 21. Determine the correct reason for “Reason B” in the proof above.
A. SAS Triangle Congruence
C. SSS Triangle Congruence
B. ASA Triangle Congruence
D. SSA Triangle Congruence
____ 22. Determine the correct reason for “Reason C” in the proof above.
A. substitution property of equality
C. SSS Triangle Congruence
B. Corresponding Parts of Congruent
Triangles are Congruent
D. Corresponding Parts of Similar
Triangles are Similar
Use the following conditional statement for the next three questions: “If a parallelogram is a
rectangle, then it has four right angles.”
____ 23. Write the converse of the conditional statement above.
A. If a parallelogram has four right
angles, then it is a rectangle.
C. If a parallelogram is not a rectangle,
then it does not have four right angles.
B. If a parallelogram is a rectangle, then it D. If a parallelogram does not have four
has four right angles.
right angles, then it is a rectangle.
____ 24. Write the inverse of the conditional above.
A. If a parallelogram is a rectangle, then it C. If a parallelogram has four right
does not have four right angles.
angles, then it is a rectangle.
B. If a parallelogram is not a rectangle,
D. If a parallelogram does not have four
then it does not have four right angles.
right angles, then it is not a rectangle.
____ 25. Write the contrapositive of the conditional statement above.
A. If a rectangle does not have four right
angles, then it is not a parallelogram.
C. If a parallelogram does not have four
right angles, then it is not a rectangle.
B. If a rectangle is not a parallelogram,
D. If a parallelogram is not a rectangle,
then it does not have four right angles.
then it does not have four right angles.