High School

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The diagonals of parallelogram WXYZ intersect at D. Select all the statements that must be true.

A. XD ≅ YD

B. ∠WXZ ≅ ∠YZX

C. XD ≅ ZD

D. ∠XDY ≅ ∠WDZ

E. XZ ≅ WY

Answer :

Final answer:

The true statements regarding the diagonals and corresponding angles of a parallelogram WXYZ intersecting at D are that XD is congruent to YD, angle XDY is congruent to angle WDZ, and side XZ is congruent to side WY.

Explanation:

The student has asked about the properties of a parallelogram and its diagonals. In parallelogram WXYZ, with diagonals intersecting at point D, certain statements about segment congruence and angle congruence can be confirmed to be true based on the properties of parallelograms.

XD⋅YD: This must be true because diagonals of a parallelogram bisect each other.

XZ⋅WY: This must be true because in a parallelogram, opposite sides are congruent.

∠XDY⋅∠WDZ: This must be true because they are alternate interior angles formed by a transversal intersecting parallel lines, and therefore they are congruent.

However, ∠WXZ⋅∠YZX and XD⋅ZD do not have to be congruent based on the information given. The first is not always true because not all parallelograms are rectangles, meaning angles can be different, and the second is already covered by the first point (XD bisects diagonal XZ and thus is only congruent to YD, not ZD).

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