Questions: Determine which of the following ratios is correct 1. A B D E=B C E F=A C D F 2. A B B C=A C D F=D E E F 3. A B D F=B C E F=A C D E 4. A B E F=B C D F=A C D E

Solution Steps

We are given two right-angled triangles, $\triangle ABC$ and $\triangle DEF$. In $\triangle ABC$, $\angle B = 90^\circ$ and $\angle C = \theta$. In $\triangle DEF$, $\angle E = 90^\circ$ and $\angle F = \theta$. Since two corresponding angles are equal, the two triangles are similar by the Angle-Angle (AA) similarity criterion.

Since $\triangle ABC \sim \triangle DEF$, the corresponding sides are proportional. Thus, we have:

$\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}$

Final Answer