Question

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ru is a midsegment of δstv. if st = z + 23 and ru = z, what is the value of z? z =

Explanation:

Step1: Recall midsegment theorem

The midsegment of a triangle is parallel to the third side and half its length. So, \( RU=\frac{1}{2}ST \).

Step2: Substitute given values

Given \( ST = z + 23 \) and \( RU = z \), substitute into the formula: \( z=\frac{1}{2}(z + 23) \).

Step3: Solve for z

Multiply both sides by 2: \( 2z=z + 23 \). Subtract \( z \) from both sides: \( 2z - z=23 \), so \( z = 23 \).

Answer:

23