Question

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gj is a midsegment of △hik. if hi = z + 18 and gj = z, what is hi? hi = \boxed{}

Explanation:

Step1: Recall Midsegment Theorem

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

Step2: Substitute given values

We know \( HI = z + 18 \) and \( GJ = z \). Substitute into the formula: \( z=\frac{1}{2}(z + 18) \).

Step3: Solve for \( z \)

Multiply both sides by 2: \( 2z=z + 18 \). Subtract \( z \) from both sides: \( z = 18 \).

Step4: Find \( HI \)

Substitute \( z = 18 \) into \( HI = z + 18 \): \( HI=18 + 18=36 \).

Answer:

\( HI = 36 \)