Question

23 what is the length of segment ik?

Explanation:

Step1: Apply the Mid - segment Theorem

The Mid - segment Theorem states that the segment connecting the mid - points of two sides of a triangle is parallel to the third side and half its length. Here, \(SR\) is the mid - segment of \(\triangle JIK\) since \(S\) is the mid - point of \(JK\) and \(R\) is the mid - point of \(JI\). Let \(IK = x\).

Step2: Set up the proportion

According to the Mid - segment Theorem, \(SR=\frac{1}{2}IK\). Given \(SR = 5\). Substitute into the formula: \(5=\frac{1}{2}x\).

Step3: Solve for \(x\)

Multiply both sides of the equation \(5=\frac{1}{2}x\) by \(2\). So, \(x = 2\times5\).

Answer:

\(10\)