Question

choose all answers that describe the quadrilateral ghij if $overline{gh}congoverline{ij}$, $overline{hi}congoverline{jg}$, and diagonals have equal length: $gi = hj$. answer attempt 1 out of 2 parallelogram rectangle rhombus square trapezoid

Explanation:

Step1: Recall parallelogram property

If opposite sides of a quadrilateral are congruent ($\overline{GH}\cong\overline{IJ}$ and $\overline{HI}\cong\overline{JG}$), then the quadrilateral is a parallelogram.

Step2: Recall rectangle property

In a parallelogram, if the diagonals are equal ($GI = HJ$), then the parallelogram is a rectangle.

Step3: Analyze rhombus condition

There is no information given about all - sides being equal, so we can't conclude it's a rhombus.

Step4: Analyze square condition

Since there is no information about all - sides being equal and angles being right - angles, we can't conclude it's a square.

Step5: Analyze trapezoid condition

A trapezoid has only one pair of parallel sides and the given information does not match the properties of a trapezoid.

Answer:

A. Parallelogram
B. Rectangle