Question

find hj.
hj =
submit
work it out
not feeling ready yet? these can help:
side lengths and angle measures in similar figures (81)
midsegments of triangles

Explanation:

Step1: Identify Similar Triangles

Since \( GI \parallel FJ \), by the Basic Proportionality Theorem (Thales' theorem), \( \triangle HGI \sim \triangle HFJ \). So, the ratios of corresponding sides are equal: \( \frac{HG}{HF} = \frac{HI}{HJ} \).

Step2: Calculate \( HF \)

\( HF = HG + GF = 26 + 39 = 65 \). Let \( HJ = x \), \( HI = 20 \). So, \( \frac{26}{65} = \frac{20}{x} \).

Step3: Solve for \( x \)

Cross - multiply: \( 26x = 65\times20 \). Then \( x=\frac{65\times20}{26}=\frac{1300}{26} = 50 \).

Answer:

\( 50 \)