Solution
Step 1:
Properties of Parallelograms Explained
1. Opposite sides are parallel. ...
2. Opposite sides are congruent. ...
3. Opposite angles are congruent. ...
4. Same-Side interior angles (consecutive angles) are supplementary. ...
5. Each diagonal of a parallelogram separates it into two congruent triangles. ...
6. The diagonals of a parallelogram bisect each other.
Step 2:
The diagonals of a parallelogram bisect each other.
[tex]\begin{gathered} The\text{ }diagonals\text{ }of\text{ }a\text{ }parallelogram\text{ }bisect\text{ }each\text{ }other. \\ w\text{ + 7 = 5w - 5} \\ and \\ \frac{3}{2x}\text{ = 3} \end{gathered}[/tex]
Step 3
[tex]\begin{gathered} Solve\text{ for w:} \\ w\text{ + 7 = 5w - 5} \\ Add\text{ similar terms} \\ 7\text{ + 5 = 5w - w} \\ 12\text{ = 4w} \\ w\text{ = }\frac{12}{4} \\ w\text{ = 3} \end{gathered}[/tex]
Step 4
[tex]\begin{gathered} Solve\text{ for x:} \\ \frac{3}{2x}\text{ = 3} \\ 3\times2x\text{ = 3} \\ \\ 6x\text{ = 3} \\ \\ x\text{ = }\frac{3}{6} \\ \\ x\text{ = }\frac{1}{2} \end{gathered}[/tex]
Final answer
[tex]\text{w = 3 . x = }\frac{1}{2}[/tex]
