Logic and Reasoning Answers
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.
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?
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.
Inductive reasoning is based on
How can the statement be rewritten as a conditional statement in if-then form?A rectangle with 4 congruent sides is a square.
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 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.
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.
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?
How can the statement be rewritten as a conditional statement in if-then form?A rectangle with 4 congruent sides is a square.
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.
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.
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.
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.
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.
Which is a counterexample for the conditional statement?If a square has side length s, then the perimeter is less than the area.
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.
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 .
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.
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