12 multiple-choice questions, progressively harder.
Which condition defines a trapezoid in this course?
Solution
Correct answer: B
The inclusive definition requires at least one opposite parallel pair. It includes parallelograms; the exactly-one condition is stronger than the definition.
Convex trapezoid ABCDABCDABCD has chosen bases ABABAB and CDCDCD. Which sides are its legs?
Correct answer: D
The bases are the chosen opposite parallel sides. The other two boundary sides, AD and BC, are the legs.
Why does a rectangle qualify as an isosceles trapezoid here?
Correct answer: A
A rectangle has parallel opposite sides and congruent right angles at a chosen base. Neither equal adjacent sides nor perpendicular diagonals is needed.
A convex isosceles trapezoid ABCDABCDABCD has bases ABABAB and CDCDCD. Its angle at AAA is 61∘61^\circ61∘. What is the angle at CCC?
Correct answer: C
The angle at B equals the angle at A. The angles at B and C along leg BC are supplementary.
A trapezoid has bases of 17 cm and 29 cm. What is the length of its midsegment?
The midsegment is the average of the base lengths.
Which endpoints define a trapezoid midsegment?
A trapezoid midsegment joins the leg midpoints. Joining base midpoints is a different segment and does not invoke this theorem.
An isosceles trapezoid has one diagonal of length 212121 cm. What is the length of the other diagonal?
Reflection in the common perpendicular bisector of the bases swaps the diagonals. They therefore have equal lengths.
In convex kite ABCDABCDABCD, the equal side pairs meet at AAA and CCC. Which diagonal is guaranteed to bisect the other?
AC connects the equal-side meeting vertices. The congruent-triangle proof makes AC the perpendicular bisector of BD; the reverse bisection needs extra information.
Convex kite ABCDABCDABCD has equal pairs meeting at AAA and CCC. Its diagonals meet at OOO, and BDBDBD is 181818 cm long. What is BOBOBO?
AC bisects BD at O, so BO is half of the whole diagonal BD.
In a convex kite, ACACAC joins the equal-side meeting vertices. The whole angle at AAA is 80∘80^\circ80∘. What is m∠BACm\angle BACm∠BAC?
AC bisects the vertex angle at A, so angle BAC is half of 80 degrees.
A convex kite ABCDABCDABCD has equal pairs meeting at AAA and CCC. Its angle at BBB is 103∘103^\circ103∘. Which angle must also measure 103∘103^\circ103∘?
SSS makes triangle ABC congruent to triangle ADC. The whole angles at B and D correspond, while the whole angles at A and C need not be congruent.
A non-parallelogram isosceles trapezoid has how many rotational symmetries, including the identity?
Only the identity works. A half-turn would interchange unequal bases, and a quarter-turn would require two opposite parallel pairs.
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