Question

1. (triangle with points a, b, c, d, e; ae=4, ed=10, eb=6, dc=x; solve for x)

Explanation:

Step1: Identify Similar Triangles

Since \( EB \parallel DC \), triangles \( AEB \) and \( ADC \) are similar by the Basic Proportionality Theorem (Thales' theorem). For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{AE}{AD}=\frac{EB}{DC}\).

Step2: Calculate \( AD \)

\( AD = AE + ED = 4 + 10 = 14 \).

Step3: Set Up Proportion

Substitute the known values into the proportion: \(\frac{4}{14}=\frac{6}{x}\).

Step4: Solve for \( x \)

Cross - multiply: \( 4x = 14\times6 \). Then \( 4x = 84 \). Divide both sides by 4: \( x=\frac{84}{4}=21 \).

Answer:

\( x = 21 \)