Question

1. find the value of x in the figure below if \\( \overline { g h } \\) is parallel to \\( \overline { j k } \\).

5 units
6.7 units
4 units
9.8 units

Explanation:

Step1: Identify the theorem

Since \( \overline{GH} \parallel \overline{JK} \), by the Basic Proportionality Theorem (Thales' theorem), the line \( JK \) divides the sides \( GI \) and \( HI \) proportionally. So, \( \frac{GJ}{JI}=\frac{HK}{KI} \).

Step2: Substitute the values

We know \( GJ = 10.5 \), \( JI = 7 \), \( HK = 7.5 \), and \( KI = x \). Substituting these values into the proportion: \( \frac{10.5}{7}=\frac{7.5}{x} \).

Step3: Solve for \( x \)

Cross - multiply: \( 10.5x=7\times7.5 \).
First, calculate \( 7\times7.5 = 52.5 \). Then, \( x=\frac{52.5}{10.5} \).
Simplify the right - hand side: \( \frac{52.5}{10.5}=5 \).

Answer:

5 units