AnswersGeometryLogic and Reasoning

Logic and Reasoning — Quiz Answers

10 verified answers
1
Free Preview

How can the statement be rewritten as a conditional statement in if-then form? A rectangle with 4 congruent sides is a square.

A
If a figure has 4 congruent sides, then it is a rectangle or square.
B
If a figure has 4 congruent sides, then it is a square.
C
If a figure is a rectangle, then it is a square.
D
If a rectangle has 4 congruent sides, then it is a square.
2
Free Preview

If the statement is rewritten as a conditional statement in if-then form, which best describes the conclusion? A student who earns 85 percent earns a B.

A
Then a student earns 85 percent
B
Then a student earns a B
C
If a student earns a B
D
If a student earns 85 percent
3

Madeline is asked to analyze the true statements shown. If two lines meet at a 90 degrees angle, they are perpendicular. If two lines are perpendicular, they have opposite reciprocal slopes. Which conclusion can Madeline draw from the given statements?

A
Based on inductive reasoning, if two lines have opposite reciprocal slopes, then they meet at a 90 degrees angle.
B
Based on the law of syllogism, if two lines have opposite reciprocal slopes, then they meet at a 90 degrees angle.
C
Based on inductive reasoning, if two lines meet at a 90 degrees angle, then they have opposite reciprocal slopes.
D
Based on the law of syllogism, if two lines meet at a 90 degrees angle, then they have opposite reciprocal slopes.
4

If the statement shown is rewritten as a conditional statement in if-then form, which best describes the conclusion? When a number is divisible by 9, the number is divisible by 3.

A
If a number is divisible by 9
B
Then the number is divisible by 3
C
If a number is divisible by 3
D
Then the number is divisible by 9
5

Galen wrote the statement "If the sum of the digits in a number is divisible by 3, the original number is divisible by 3." Which statements are true regarding his work? Choose three correct answers.

A
The conclusion of the statement is written before the hypothesis.
B
An equivalent statement is "If the sum of the digits in a number is divisible by 3, then the original number is divisible by 3."
C
The hypothesis of the statement is "the sum of the digits in a number is divisible by 3."
D
The statement is not a conditional statement because it does not include both an "if" and a "then" clause.
E
The statement can be proven true or false.
6

Holly wrote the statement Polygon R S T U V is regular if it has congruent sides and congruent angles. Which statements are true regarding her work? Choose three correct answers.

A
The hypothesis of the statement is "it has congruent sides and congruent angles."
B
It is a conditional statement.
C
The statement cannot be proven true or false.
D
The conclusion of the statement is "Polygon R S T U V is regular."
E
An equivalent statement is "If polygon R S T U V has congruent sides, then it has congruent angles."
7

Inductive reasoning is based on

A
rules.
B
facts.
C
patterns.
D
definitions.
8

How can the statement be rewritten as a conditional statement in if-then form? The sum of the digits of a two-digit number is less than the value of the original two-digit number.

A
If a number has two digits, then the value of the original two-digit number is less than the sum of its digits.
B
If the sum of the digits of a number is less than the value of the original number, then the number is a two-digit number.
C
If a number has two digits, then the sum of its digits is less than the value of the original two-digit number.
D
If the sum of the digits of a two-digit number is less than the value of the original two-digit number, then the value of the original two-digit number is greater than the sum of the two digits.
9

Which conclusion can be drawn based on the true statements shown? If a line segment is a diameter, then it is the longest chord in a circle. Line segment A B is a diameter.

A
Based on the law of detachment, the longest chord in a circle is a diameter.
B
Based on the law of syllogism, line segment A B is the longest chord in a circle.
C
Based on the law of detachment, line segment A B is the longest chord in a circle.
D
Based on the law of syllogism, the longest chord in a circle is a diameter.
10

Mr. Thomas wrote these true statements. If a figure is a triangle, the sum of the figure's interior angles is 180 degrees Figure A B C is a triangle. Which conclusion can be drawn?

A
Using the law of detachment, if the sum of a figure’s interior angles is 180 degrees , then the figure is a triangle.
B
Using inductive reasoning, if the sum of a figure’s interior angles is 180 degrees , then the figure is a triangle.
C
Using inductive reasoning, the sum of the interior angles of A B C is 180 degrees .
D
Using the law of detachment, the sum of the interior angles of A B C is 180 degrees .

Did you find these answers helpful?

Logic and Reasoning — Quiz Answers — Geometry