12 multiple-choice questions, progressively harder.
A problem says “Given: M is the midpoint of segment PQ. Prove: PM = MQ.” Which fact may be used at the start?
Solution
Correct answer: C
A proof starts from the supplied givens.
The equality is the requested goal; it must follow from the midpoint definition rather than being assumed.
Which reason justifies AB + BC = AC?
Correct answer: A
Segment addition needs the two smaller segments to form the larger segment.
Betweenness of B on AC supplies that condition.
From AB=CDAB=CDAB=CD, a proof writes CD=ABCD=ABCD=AB. Which property is used?
Correct answer: D
Symmetry reverses the order of an equality.
It does not add a quantity or claim that a segment is part of another.
A proof uses JK=JKJK=JKJK=JK. Which reason applies?
Correct answer: B
A numerical length equals itself.
This is the reflexive property; no midpoint or angle condition is involved.
If a=ba=ba=b and b=cb=cb=c, which conclusion follows by transitivity?
The equalities connect a to b and b to c.
Transitivity joins them to give a=c.a=c.a=c.
Segments AB and CD are given to be congruent. Which equality follows?
Congruent segments have equal lengths by definition.
The plain letter pairs in the equality denote lengths, not the endpoints themselves.
A proof has EF=GHEF=GHEF=GH, EF=23EF=23EF=23, and GH=x+6GH=x+6GH=x+6. Which equation follows by substitution?
Replace each length in EF = GH by its given expression.
That gives 23=x+6.23=x+6.23=x+6.
Which proof format pairs statements with reasons in adjacent columns?
A two-column proof places each statement beside the justification for it.
The structure helps reveal missing reasons, but it does not replace them.
What do arrows in a flow proof indicate?
A flow proof organizes dependencies between statements.
The arrows belong to the argument, not to the geometric givens.
What is temporarily assumed in proof by contradiction?
A contradiction proof tests whether the goal could be false while the givens remain true.
It must then derive an impossibility and reject that temporary assumption.
A point is given only to be on segment AB. May it be marked as the midpoint?
The location supplies only one midpoint condition.
The two part lengths must also be equal.
What makes a direct proof complete?
A proof is a connected argument whose steps are supported.
Its length and presentation do not guarantee that the goal follows.
Reset this practice set?
This clears every answer you have given and starts the set again from question 1.