Question

in △ghi and △jkl, if ∠g≅∠j, gh = 10, gi = 15, and jk = 5, what is the missing side jl?
a. 7.5 cm
b. 7 cm
c. 10 cm
d. 8.5 cm

Explanation:

Step1: Determine similarity

Since \(\angle G\cong\angle J\), assume \(\triangle GHI\sim\triangle JKL\) (by AA similarity if other angles are equal, which is implied in such problems).

Step2: Set up proportion

For similar triangles, \(\frac{GH}{JK}=\frac{GI}{JL}\). Substitute \(GH = 10\), \(GI=15\), \(JK = 5\) into the proportion: \(\frac{10}{5}=\frac{15}{JL}\).

Step3: Solve for \(JL\)

Cross - multiply: \(10\times JL=5\times15\), so \(10JL = 75\). Then \(JL=\frac{75}{10}=7.5\).

Answer:

a. \(7.5\mathrm{cm}\)