Question

what is the value of u?
triangle with segments labeled 2u, u+16, and right angle at y, with x, y, v, w labeled vertices and markings indicating congruent segments
u = \square

Explanation:

Step1: Apply the perpendicular bisector theorem

Since \(W\) is the mid - point of \(XV\) (marked as equal segments) and \(WY\perp XV\), by the perpendicular bisector theorem of a triangle (a point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment), we have \(VX = VX\) (common side), \(WX=WV\) (mid - point and perpendicular), so \(2u=u + 16\).

Step2: Solve the equation for \(u\)

Subtract \(u\) from both sides of the equation \(2u=u + 16\).

$$2u-u=u + 16-u$$

$$u = 16$$

Answer:

\(16\)