Similarity, SMB-020

Prove that this pair of triangles are similar. (3 marks)

--- 6 WORK AREA LINES (style=lined) ---

Show Answers Only

\(\text{Proof (See Worked Solution)}\)

Show Worked Solution

\(\text{Find unknown side}\ (x)\ \text{of smaller triangle}\)

\(\text{Using Pythagoras:}\)

\(x=\sqrt{5^2-4^2} = \sqrt{9} = 3\)

\(\dfrac{AC}{DE} = \dfrac{5}{15} = \dfrac{1}{3} \)

\(\dfrac{BC}{EF} = \dfrac{3}{9} = \dfrac{1}{3} \)

\(\angle ABC = \angle DEF = 90^{\circ} \ \ \text{(given)} \)

\(\therefore \Delta ABC\ \text{|||}\ \Delta DEF\ \ \text{(hypotenuse and second side of right-angled triangle in proportion)}\)