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Answer :
- Set up the equation $2x + 5 = 3x + 2$ based on the property that diagonals of a parallelogram bisect each other.
- Subtract $2x$ from both sides to get $5 = x + 2$.
- Subtract $2$ from both sides to solve for $x$, resulting in $x = 3$.
- Conclude that for WXYZ to be a parallelogram, $\boxed{x = 3}$.
### Explanation
1. Understanding the properties of a parallelogram
In a parallelogram, the diagonals bisect each other. This means that the point of intersection divides each diagonal into two equal segments. In quadrilateral WXYZ, if C is the intersection of diagonals WY and XZ, then for WXYZ to be a parallelogram, WC must equal CY. We are given that WC = 2x + 5 and CY = 3x + 2.
2. Setting up the equation
To find the value of x that makes WXYZ a parallelogram, we set WC equal to CY:
$$2x + 5 = 3x + 2$$
3. Subtracting 2x from both sides
Now, we solve the equation for x. First, subtract 2x from both sides of the equation:
$$2x + 5 - 2x = 3x + 2 - 2x$$
$$5 = x + 2$$
4. Subtracting 2 from both sides
Next, subtract 2 from both sides of the equation:
$$5 - 2 = x + 2 - 2$$
$$3 = x$$
So, x = 3.
5. Final Answer
Therefore, for quadrilateral WXYZ to be a parallelogram, x must equal 3.
### Examples
Understanding parallelograms is useful in construction and design. For example, when building a bridge, engineers use the properties of parallelograms to ensure structural stability. The equal and parallel sides help distribute weight evenly, preventing collapse. Similarly, architects use parallelograms in building designs for aesthetic appeal and structural integrity.
- Subtract $2x$ from both sides to get $5 = x + 2$.
- Subtract $2$ from both sides to solve for $x$, resulting in $x = 3$.
- Conclude that for WXYZ to be a parallelogram, $\boxed{x = 3}$.
### Explanation
1. Understanding the properties of a parallelogram
In a parallelogram, the diagonals bisect each other. This means that the point of intersection divides each diagonal into two equal segments. In quadrilateral WXYZ, if C is the intersection of diagonals WY and XZ, then for WXYZ to be a parallelogram, WC must equal CY. We are given that WC = 2x + 5 and CY = 3x + 2.
2. Setting up the equation
To find the value of x that makes WXYZ a parallelogram, we set WC equal to CY:
$$2x + 5 = 3x + 2$$
3. Subtracting 2x from both sides
Now, we solve the equation for x. First, subtract 2x from both sides of the equation:
$$2x + 5 - 2x = 3x + 2 - 2x$$
$$5 = x + 2$$
4. Subtracting 2 from both sides
Next, subtract 2 from both sides of the equation:
$$5 - 2 = x + 2 - 2$$
$$3 = x$$
So, x = 3.
5. Final Answer
Therefore, for quadrilateral WXYZ to be a parallelogram, x must equal 3.
### Examples
Understanding parallelograms is useful in construction and design. For example, when building a bridge, engineers use the properties of parallelograms to ensure structural stability. The equal and parallel sides help distribute weight evenly, preventing collapse. Similarly, architects use parallelograms in building designs for aesthetic appeal and structural integrity.
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