Question

8.
2x - 8
x + 17

Explanation:

Step1: Identify the theorem

The figure shows a triangle with a midline (the segment with length \(2x - 8\)) and the base of the triangle (or the side of the parallelogram) with length \(x + 17\). By the Midline Theorem (also called the Midsegment Theorem) in triangles, the midline is parallel to the third side and half its length. Wait, actually, if the quadrilateral is a parallelogram (since the sides are marked congruent), then the midline segment and the side \(x + 17\) should be equal? Wait, no, looking at the markings: the two sides of the triangle are marked with two ticks (so the segment \(2x - 8\) connects the midpoints of the two sides of the triangle), so by the Midline Theorem, the length of the midline is half the length of the third side. Wait, but the quadrilateral on the right: if the triangle has a midline, and the other figure is a parallelogram (since the opposite sides are marked congruent), then maybe \(2x - 8\) is equal to \(x + 17\)? Wait, no, let's re - examine. The midline of a triangle is parallel to the third side and its length is half the length of the third side. But in the diagram, the segment \(2x - 8\) and the side \(x + 17\): if the quadrilateral is a parallelogram (because the two pairs of opposite sides are marked congruent), then the midline segment (which is parallel to the base) and the side of the parallelogram should be equal? Wait, maybe the correct approach is that the midline (the segment connecting the midpoints of two sides of a triangle) is equal to half the length of the third side. But in this case, if the quadrilateral is a parallelogram, then the length of the midline (\(2x - 8\)) should be equal to the length of the side of the parallelogram (\(x + 17\))? Wait, no, let's set up the equation. Wait, maybe the two segments \(2x - 8\) and \(x + 17\) are equal because of the midline or the parallelogram properties. Let's assume that \(2x-8=x + 17\).

Step2: Solve the equation

We have the equation \(2x-8=x + 17\).
Subtract \(x\) from both sides: \(2x-x-8=x - x+ 17\), which simplifies to \(x-8 = 17\).
Then add 8 to both sides: \(x-8 + 8=17 + 8\), so \(x=25\).

Answer:

\(x = 25\)