Question

given kite abcd and isosceles trapezoid wxyz, complete a two - column proof to show that △adw≅△cdz.
which of the following is given from the figure? select all that apply.
□ a. (overline{ac}paralleloverline{wz})
□ b. (overline{ab}paralleloverline{cd})
□ c. (overline{dw}congoverline{ac})
□ d. (overline{dw}congoverline{dz})

Explanation:

Step1: Analyze the properties of a kite

In kite \(ABCD\), \(AB = BC\) and \(AD=CD\) (by the definition of a kite, two - pairs of adjacent sides are equal).

Step2: Analyze the properties of an isosceles trapezoid

In isosceles trapezoid \(WXYZ\), \(WX = YZ\) and \(XY\parallel WZ\). Also, since it is an isosceles trapezoid, the non - parallel sides are equal and the base angles are equal.

Step3: Check the given options

• Option A: There is no information in the figure or the problem statement to suggest that \(\overline{AC}\parallel\overline{WZ}\).
• Option B: In a kite \(ABCD\), by the definition of a kite, \(\overline{AB}\) is not parallel to \(\overline{CD}\).
• Option C: There is no indication that \(\overline{DW}\cong\overline{AC}\).
• Option D: In isosceles trapezoid \(WXYZ\), if \(D\) is the mid - point of \(WZ\) (which is a reasonable assumption based on the symmetry of the figure for the congruence proof of \(\triangle ADW\cong\triangle CDZ\)), then \(\overline{DW}\cong\overline{DZ}\).

Answer:

D. \(\overline{DW}\cong\overline{DZ}\)