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

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=√(3) \\ (√(3))/(2)EF=(√(3))/(2)*2=√(3) \\ EG=(√(3))/(2)EF \end{gathered}`

Option E

`\begin{gathered} EG=√(3) \\ √(3)FG=√(3)*1=√(3) \\ \implies EG=√(3)FG \end{gathered}`

Option F

`\begin{gathered} EF=2 \\ 2FG=2*1=2 \\ \implies EF=2FG \end{gathered}`

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