Question

1. image of two triangles (one with vertices a, b, c, right angle at b, side ac=15, bc=9; another with vertices d, e, f, right angle at e, side ef=6, side df=x; angles at a and d, angles at c and f are equal) scale factor= ____ missing side length = ____

Explanation:

Step1: Identify Corresponding Sides

Triangles \(ABC\) and \(DEF\) are similar (same angles \(m\) and \(n\), right angles at \(B\) and \(E\)). Corresponding sides: \(BC = 9\) and \(EF = 6\).

Step2: Calculate Scale Factor

Scale factor is \(\frac{EF}{BC}=\frac{6}{9}=\frac{2}{3}\).

Step3: Find Missing Side \(x\)

Corresponding side to \(AC = 15\) is \(DF = x\). Using scale factor: \(x = AC\times\frac{2}{3}=15\times\frac{2}{3}=10\).

Answer:

Scale Factor = \(\frac{2}{3}\)
Missing Side length = \(10\)