The quadrilateral ABCD is a square.

Here's the step-by-step explanation:

1. The diagonals of a quadrilateral divide it into four triangles. If these triangles have equal areas, then each pair of opposite triangles are congruent (have the same size and shape).

2. In a quadrilateral, if the diagonals bisect each other (intersect at their midpoints), the quadrilateral is a parallelogram.

3. In a parallelogram, if the diagonals are of equal length, then it is a rectangle.

4. In a rectangle, if the sides are of equal length, then it is a square.

5. Therefore, if the diagonals of a quadrilateral bisect each other and divide the quadrilateral into four triangles of equal area, the quadrilateral is a square.

Question

The quadrilateral ABCD is a square.

Here's the step-by-step explanation:

1. The diagonals of a quadrilateral divide it into four triangles. If these triangles have equal areas, then each pair of opposite triangles are congruent (have the same size and shape).

2. In a quadrilateral, if the diagonals bisect each other (intersect at their midpoints), the quadrilateral is a parallelogram.

3. In a parallelogram, if the diagonals are of equal length, then it is a rectangle.

4. In a rectangle, if the sides are of equal length, then it is a square.

5. Therefore, if the diagonals of a quadrilateral bisect each other and divide the quadrilateral into four triangles of equal area, the quadrilateral is a square.

Knowee AI · Accepted Answer

The quadrilateral ABCD is a square.

Here's the step-by-step explanation:

1. The diagonals of a quadrilateral divide it into four triangles. If these triangles have equal areas, then each pair of opposite triangles are congruent (have the same size and shape).

2. In a quadrilateral, if the diagonals bisect each other (intersect at their midpoints), the quadrilateral is a parallelogram.

3. In a parallelogram, if the diagonals are of equal length, then it is a rectangle.

4. In a rectangle, if the sides are of equal length, then it is a square.

5. Therefore, if the diagonals of a quadrilateral bisect each other and divide the quadrilateral into four triangles of equal area, the quadrilateral is a square.

If the diagonals AC and BD of a quadrilateral ABCD, intersect at D and separate the quadrilateral into four triangles of equal area, then the quadrilateral ABCD is

Question

Solution

Similar Questions

Upgrade your grade with Knowee