12 multiple-choice questions, progressively harder.
Which description is a definition rather than a report about a drawing?
Solution
Correct answer: B
A definition fixes the meaning of a term.
The rectangle description lists the exact membership conditions. The other statements concern particular observations.
A quadrilateral has four right angles and four congruent sides. Which classification agrees with the lesson definitions?
Correct answer: D
Four right angles meet the rectangle definition.
Having four congruent sides as well meets the square definition. Inclusive definitions allow both names.
What does a counterexample to “Every rectangle is a square” need to be?
Correct answer: A
The hypothesis restricts the claim to rectangles.
A counterexample must be in that family and fail the proposed conclusion, so it must not be a square.
A conjecture matches every one of 50 measurements. What is established by those measurements alone?
Correct answer: C
Measurements give evidence about the cases tested and have limited precision.
They do not justify an exact claim for every allowed figure.
Which comparison correctly distinguishes an accepted postulate from a proved result?
The unique-line statement is an accepted incidence postulate.
If two distinct lines shared two distinct points, that postulate would make them the same line. Thus the at-most-one-point result is proved from the accepted foundation.
In “If M is the midpoint of segment AB, then AM = MB,” what is the hypothesis?
The hypothesis is the condition following “if.”
The equality following “then” is the conclusion.
Which is the converse of “If a figure is a square, then it is a rectangle”?
A converse exchanges the hypothesis and conclusion.
It says rectangle implies square, which is a separate claim from the original.
Which is the inverse of “If an angle is right, then its measure is 90 degrees”?
An inverse negates both parts without reversing their order.
The hypothesis stays about being right; the conclusion stays about measuring 90 degrees.
Which form is logically equivalent to a conditional in every case?
A conditional and its contrapositive exclude the same failure: a true hypothesis with a false conclusion.
The converse and inverse need not agree with the original.
What does “p if and only if q” promise?
A biconditional combines a conditional and its converse.
Each direction needs a justification.
Every square is a rectangle. Figure H is a square. Which conclusion follows by detachment?
The given figure satisfies the hypothesis of the conditional.
Detachment supplies its conclusion for that figure: H is a rectangle.
You know u→vu\to vu→v and v→wv\to wv→w. Which conditional follows by syllogism?
The conclusion vvv of the first conditional matches the hypothesis vvv of the second.
Following both links gives u→wu\to wu→w. The premises do not justify reversing either link.
Reset this practice set?
This clears every answer you have given and starts the set again from question 1.