Identifying a Parallelogram: Identification by diagonals

To determine whether quadrilateral ABCD is a parallelogram, we examine the segments of its diagonals.

• Measure segments $AF$ and $FD$ on diagonal $AD$.
• Measure segments $BF$ and $FC$ on diagonal $BC$.

We have:

• $AF = 4$ and $FD = 6$.
• $BF = 2$ and $FC = 3$.

A necessary condition for ABCD to be a parallelogram is that its diagonals bisect each other:

• This requires $AF = FD$ and $BF = FC$.

Here, $AF$ is not equal to $FD$ and $BF$ is not equal to $FC$, which means the diagonals do not bisect each other.

Therefore, quadrilateral ABCD is not a parallelogram.

The correct answer is No.

To determine if quadrilateral $ABCD$ is a parallelogram, we need to verify if its diagonals $AC$ and $BD$ bisect each other. This can be confirmed if their respective segments around intersection point $F$ are equal.

Given the information, we have:

• $AF = 2$ and $FD = 2$, indicating diagonal $AD$ is bisected by $F$.
• $BF = 5$ and $FC = 5$, indicating diagonal $BC$ is bisected by $F$.

Since both conditions are satisfied, the diagonals indeed bisect each other, fulfilling the criteria for quadrilateral $ABCD$ to be a parallelogram.

Therefore, the answer to the question is Yes, quadrilateral $ABCD$ is a parallelogram.

To determine if the quadrilateral ABCD is a parallelogram, we must consider the properties of its diagonals. One key property of parallelograms is that the diagonals bisect each other.

We are given $AF = 5$, $FD = 6$, $BF = 7$, and $FC = 7$. These segments imply the diagonals intersect at point F. To be a parallelogram, each pair of opposite triangle segments created should be equal.

Checking for bisected diagonals:
- For diagonal $AC$, segments $AF = 5$ and $FC = 7$ are not equal.
- For diagonal $BD$, segments $BF = 7$ and $FD = 6$ are also not equal.

Since neither diagonal is divided into equal lengths by point F, diagonals AC and BD do not bisect each other.

Therefore, quadrilateral ABCD does not meet the condition of diagonals bisecting one another and cannot be classified as a parallelogram.

No.