Question

1. find the value of x in the figure below if \\(\overline{gh}\\) is parallel to \\(\overline{jk}\\).

Explanation:

Step1: Identify similar triangles

Since $\overline{GH} \parallel \overline{JK}$, $\triangle IJK \sim \triangle IGH$ by AA similarity.

Step2: Set up proportion

Corresponding sides are proportional: $\frac{IJ}{IG} = \frac{IK}{IH}$
$\frac{7}{10.5} = \frac{x}{7.5}$

Step3: Solve for x

Cross-multiply: $10.5x = 7 \times 7.5$
$10.5x = 52.5$
$x = \frac{52.5}{10.5} = 5$

Answer:

5