Question

identifying the properties of trapezoids
which statements are correct regarding the properties of trapezoids? choose two correct answers.
the diagonals of a trapezoid are perpendicular.
base angles of a trapezoid are congruent.
the adjacent sides of a trapezoid are congruent.
the diagonals of an isosceles trapezoid are congruent.
the bases of a trapezoid are parallel.

Explanation:

• For "The diagonals of an isosceles trapezoid are congruent":
• In an isosceles trapezoid, by its definition (a trapezoid with non - parallel sides equal), using triangle congruence (e.g., \(\triangle ABC\cong\triangle BAD\) if \(AD = BC\), \(AB=BA\), and \(\angle ABC=\angle BAD\) for trapezoid \(ABCD\) with \(AD\parallel BC\)), we can show that the diagonals \(AC\) and \(BD\) are congruent.
• For "The bases of a trapezoid are parallel":
• The definition of a trapezoid is a quadrilateral with exactly one pair of parallel sides. These parallel sides are called the bases of the trapezoid.

• For "The diagonals of a trapezoid are perpendicular":
• In a general trapezoid, there is no property that guarantees the diagonals are perpendicular. This is only true for some special cases (e.g., in a right trapezoid with some specific side - length ratios, but not in all trapezoids).
• For "Base angles of a trapezoid are congruent":
• This is only true for isosceles trapezoids. In a non - isosceles trapezoid, the base angles are not congruent.
• For "The adjacent sides of a trapezoid are congruent":
• In a general trapezoid, adjacent sides (the non - parallel sides and the sides connecting the bases) are not congruent. This is a property of some special quadrilaterals like rhombuses or squares (which are not trapezoids in the strict sense of having exactly one pair of parallel sides for non - degenerate trapezoids).

Answer:

The diagonals of an isosceles trapezoid are congruent; The bases of a trapezoid are parallel.