Question

what is the value of u?
there is a geometric figure with points a, b, c, d. angle at a and angle at c are right angles. segment da is labeled 2u - 26, segment dc is labeled u + 4. there are some lines from d to b and other connections.

Explanation:

Step1: Use the Angle - Angle - Side (AAS) congruence

Since \( \angle A=\angle C = 90^{\circ}\), \( \angle ABD=\angle CBD\), and \(BD = BD\) (common side), \(\triangle ABD\cong\triangle CBD\) by AAS congruence.

Step2: Set up the equation

For congruent triangles \(\triangle ABD\) and \(\triangle CBD\), the corresponding sides are equal. So \(AD = CD\). Given \(AD = 2u - 26\) and \(CD=u + 4\), we have the equation \(2u-26=u + 4\).

Step3: Solve the equation

Subtract \(u\) from both sides: \(2u-u-26=u - u+ 4\), which simplifies to \(u-26 = 4\).
Add 26 to both sides: \(u-26 + 26=4 + 26\).

Answer:

\(u = 30\)