15
QuizMultiple Choice

Mathematical Modeling: Part Four — Test

Question 15 • Mathematics III

If quadrilateral ABCD is an isosceles trapezoid, which statements must be true? Choose three correct answers.

Answer
A
line segment BA is congruent to line segment CD
B
line segment BE is congruent to line segment ED
C
line segment BD perpendicular to line segment AC
D
angle CBA is congruent to angle BCD
E
line segment BC is parallel to line segment AD

Explanation

In an isosceles trapezoid, the bases are parallel, so BC is parallel to AD. Its legs are congruent, so BA is congruent to CD. The base angles at B and C are also congruent, giving ∠CBA ≅ ∠BCD. The diagonals do not generally bisect each other or meet at right angles, so the statements about BE and ED and perpendicular diagonals need not be true.

AI-written and checked against the verified answer.

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