Question

choose all answers that describe the quadrilateral ghij if ∠g≅∠h≅∠i≅∠j and diagonals are perpendicular: (overline{gi}perpoverline{hj}). answer attempt 1 out of 2 parallelogram rectangle rhombus square trapezoid

Explanation:

Step1: Analyze angle - equality property

Since $\angle G\cong\angle H\cong\angle I\cong\angle J$, and the sum of interior angles of a quadrilateral is $360^{\circ}$, then each angle is $\frac{360^{\circ}}{4}=90^{\circ}$. A quadrilateral with four right - angles is a rectangle.

Step2: Analyze diagonal property

The diagonals $GI\perp HJ$, i.e., the diagonals of the quadrilateral are perpendicular. A rectangle with perpendicular diagonals is a square.

Step3: Recall definitions of other quadrilaterals

A square is also a parallelogram (since opposite sides are parallel and equal), and a square is also a rhombus (since all sides are equal and diagonals are perpendicular bisectors of each other). A trapezoid has only one pair of parallel sides, and this quadrilateral does not meet that criterion.

Answer:

A. Parallelogram
B. Rectangle
C. Rhombus
D. Square