Question

1. in quadrilateral math, mt and ah bisect each other at r and mr ≅ hr. math must be a

i. parallelogram
ii. rectangle
iii. square

Explanation:

Step1: Recall the property of a parallelogram

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. In quadrilateral \(MATH\), \(MT\) and \(AH\) bisect each other at \(R\) (\(MR = HR\) and \(TR=AR\)). So, by the theorem "If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram", \(MATH\) is a parallelogram.

Step2: Analyze for rectangle and square

For a quadrilateral to be a rectangle, it needs to be a parallelogram with one - right angle or diagonals equal. For a quadrilateral to be a square, it needs to be a rectangle with adjacent sides equal. There is no information given about the angles (\(90^{\circ}\)) or the lengths of the sides (\(MA = AT\)) or the equality of the diagonals (\(MT=AH\)).

Answer:

I. parallelogram