Let's find the value of each variable one at a time.
Value of x
Notice that the sides with lengths 2x-1 and 4x-17 are opposite sides. Recall the Parallelogram Opposite Sides Theorem says that if a quadrilateral is a parallelogram, then its opposite sides are congruent. Therefore, for the figure to be a parallelogram, the lengths of the opposite sides must be equal.
2x-1=4x-17Let's solve it!
In a parallelogram, the diagonal divides the figure into two congruent triangles. Let's have a look at the given parallelogram. For convenience reasons, we will name the vertices.
For the quadrilateral to be a parallelogram, we need the triangles that make it to be congruent.
△ ABD ≅ △ CDB
The triangles share the side BD and we have already found the value of x for which AB ≅ CD. As we can see, ∠ABD and ∠CDB are included between the congruent sides. If we show that they are congruent, then △ ABD ≅ △ CDB by Side-Angle-Side Congruence Theorem.
5y-13=3y+5
Let's find the value of y for which the angles are congruent.
