Question

In A EFG, m2 E = 30°, mz F = 60°, and m² G = 90°. Which of the following statements about AEFG are true? Check all that apply.

Answer 1

Answer:

Options D, E, and F

Explanation:

Since the angles of triangle EFG are 30-60-90, this is a special triangle,

So, first, a diagram of the triangle is given below:

Next, we show the options that are true:

Option D

$\begin{gathered} EG=\sqrt{3} \\ \frac{\sqrt{3}}{2}EF=\frac{\sqrt{3}}{2}\times2=\sqrt{3} \\ EG=\frac{\sqrt{3}}{2}EF \end{gathered}$

Option E

$\begin{gathered} EG=\sqrt{3} \\ \sqrt{3}FG=\sqrt{3}\times1=\sqrt{3} \\ \implies EG=\sqrt{3}FG \end{gathered}$

Option F

$\begin{gathered} EF=2 \\ 2FG=2\times1=2 \\ \implies EF=2FG \end{gathered}$

Options D, E, and F are true about triangle EFG.