Answers FL-1206310-Geometry A - FlexLogic and Reasoning

Logic and Reasoning Answers

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Inductive reasoning is based on

definitions.

facts.

patterns.

rules.

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Madeline is asked to analyze the true statements shown.If two lines meet at a 90 angle, they are perpendicular.If two lines are perpendicular, they have opposite reciprocal slopes.

Based on the law of syllogism, if two lines meet at a 90 angle, then they have opposite reciprocal slopes.

Based on the law of syllogism, if two lines have opposite reciprocal slopes, then they meet at a 90 angle.

Based on inductive reasoning, if two lines meet at a 90 angle, then they have opposite reciprocal slopes.

Based on inductive reasoning, if two lines have opposite reciprocal slopes, then they meet at a 90 angle.

Which is a counterexample for the conditional statement?If two positive numbers are multiplied together, then the product will be greater than both of the two positive numbers.

2 x 4

5 x (−3)

Option

Which is a counterexample for the conditional statement?If a square has side length s, then the perimeter is less than the area.

s = 3

s = 5

s = 7

s = 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 AB is a diameter.

Based on the law of syllogism, line segment AB is the longest chord in a circle.

Based on the law of detachment, line segment AB is the longest chord in a circle.

Based on the law of syllogism, the longest chord in a circle is a diameter.

Based on the law of detachment, the longest chord in a circle is a diameter.

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

If a student earns 85%

If a student earns a B

Then a student earns 85%

Then a student earns a B

Which is a counterexample for the conditional statement shown?If three distinct points lie in a plane, then the points can form a triangle.

The points form a different polygon.

The points form a circle.

The points form an open figure.

The points form a line.

Inductive reasoning is based on

definitions.

facts.

patterns.

rules.

Which statement can be concluded using the true statements shown?If two angles in a triangle measure and x degrees, then the third angle measures (90 − x) degrees.In triangle ABC, angle A measures 90 degrees and angle B measures .

Angle C must measure 50 degrees.

Angle C must measure 40 degrees.

Angle C must measure (90 − 40) degrees.

Angle C must measure (90 − 30) degrees.

Mr. Thomas wrote these true statements.If a figure is a triangle, the sum of the figure's interior angles is 180.Figure ABC is a triangle.

Using the law of detachment, the sum of the interior angles of ABC is 180.

Using the law of detachment, if the sum of a figure’s interior angles is 180, then the figure is a triangle.

Using inductive reasoning, the sum of the interior angles of ABC is 180.

Using inductive reasoning, if the sum of a figure’s interior angles is 180, then the figure is a triangle.

Holly wrote the statement Polygon RSTUV is regular if it has congruent sides and congruent angles.Which statements are true regarding her work? Select three options.The hypothesis of the statement is "it has congruent sides and congruent angles."The conclusion of the statement is "Polygon RSTUV is regular."An equivalent statement is "If polygon RSTUV has congruent sides, then it has congruent angles."The statement cannot be proven true or false.It is a conditional statement.

The hypothesis of the statement is "it has congruent sides and congruent angles."

The conclusion of the statement is "Polygon RSTUV is regular."

An equivalent statement is "If polygon RSTUV has congruent sides, then it has congruent angles."

The statement cannot be proven true or false.

It is a conditional statement.

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

If a rectangle has 4 congruent sides, then it is a square.

If a figure has 4 congruent sides, then it is a square.

If a figure has 4 congruent sides, then it is a rectangle or square.

If a figure is a rectangle, then it is a square.

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.

Then the number is divisible by 3

Then the number is divisible by 9

If a number is divisible by 3

If a number is divisible by 9

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? Select three options.

The hypothesis of the statement is "the sum of the digits in a number is divisible by 3."

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."

The statement is not a conditional statement because it does not include both an "if" and a "then" clause.

The statement can be proven true or false.

The conclusion of the statement is written before the hypothesis.

Which is a counterexample for the conditional statement shown?If two distinct points are graphed on a coordinate plane, then the line connecting the points can be represented with a function.

The points have the same x-coordinate value.

The points have the same y-coordinate value.

The points follow the rule (x, y) (–x, –y).

The points follow the rule (x, y) (–y, –x).

Which conclusion can be drawn based on the true statements shown?If a triangle is equilateral, then all the sides in the triangle are congruent.If all the sides in a triangle are congruent, then all the angles are congruent.

Based on the law of syllogism, if all the angles in a triangle are congruent, then the triangle is equilateral.

Based on the law of detachment, if all the angles in a triangle are congruent, then the triangle is equilateral.

Based on the law of syllogism, if a triangle is equilateral, then all the angles are congruent.

Based on the law of detachment, if a triangle is equilateral, then all the angles are congruent.

Branden and Janna are analyzing the same conditional statement. Branden finds multiple examples that validate the conditional statement. Janna finds one example that satisfies the hypothesis of the conditional statement, but not the conclusion. Which must be true?

The conditional statement is true. There are more examples that validate the statement than there are that do not.

The conditional statement is true. There is at least one example that validates the statement.

The conditional statement is false. There is at least one counterexample for the statement.

The conditional statement is false. There must be exactly one example that validates the statement.

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.

If a number has two digits, then the sum of its digits is less than the value of the original two-digit number.

If a number has two digits, then the value of the original two-digit number is less than the sum of its digits.

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.

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.

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