The quadrilateral FGHI is a square because it has four congruent sides, all right angles, and perpendicular diagonals. Option 4 is the right choice.
As per given information,
The quadrilateral labeled FGHI, with the following properties given:
FG || HI (FG is parallel to HI)
FG = HI (FG is congruent to HI)
FH ⊥ GI (diagonals FH and GI are perpendicular)
Analyze the properties of different quadrilaterals
We can now analyze the properties of different quadrilaterals to see which ones match the given properties:
Parallelogram: A parallelogram has opposite sides parallel and congruent. In this case, we are given that FG || HI, but not that the opposite sides are congruent. So, this quadrilateral cannot be a parallelogram.
Rectangle: A rectangle is a special type of parallelogram where all angles are right angles. Since we are not given that any of the angles in the quadrilateral are right angles, this cannot be a rectangle.
Rhombus: A rhombus is a quadrilateral with all four sides congruent and all angles oblique (not right angles). We are given that FG = HI, but not that all sides are congruent. Also, we are not given any information about the angles. So, this cannot be a rhombus.
Square: A square is a special type of rhombus where all angles are right angles. Since we are given that FH ⊥ GI (diagonals are perpendicular), this implies that all angles in the quadrilateral are right angles. Additionally, we are given that FG = HI, which means all sides are congruent. Therefore, this quadrilateral satisfies all the properties of a square.
Trapezoid: A trapezoid is a quadrilateral with at least one pair of opposite sides parallel. We are given that FG || HI, so this quadrilateral could be a trapezoid. However, we are also given that the diagonals are perpendicular, which is not a property of trapezoids.
Based on the analysis above, the only quadrilateral that matches all the given properties is a square.
Option 4 is the right choice