Question

3 select all the correct answers. triangle abc is an equilateral triangle with mid - points d, e, and f of its sides ac, ba, and cb, respectively. which lines are lines of symmetry of △abc? bd ef fd af ce de

Explanation:

Step1: Recall property of equilateral - triangle symmetry

An equilateral triangle has 3 lines of symmetry which are the lines connecting each vertex to the mid - point of the opposite side.

Step2: Analyze each option

• $\overleftrightarrow{BD}$: $BD$ is the line connecting vertex $B$ to the mid - point $D$ of the opposite side $AC$, so it is a line of symmetry.
• $\overleftrightarrow{EF}$: $EF$ is not a line of symmetry as it does not connect a vertex to the mid - point of the opposite side.
• $\overleftrightarrow{FD}$: $FD$ is not a line of symmetry as it does not connect a vertex to the mid - point of the opposite side.
• $\overleftrightarrow{AF}$: $AF$ is the line connecting vertex $A$ to the mid - point $F$ of the opposite side $CB$, so it is a line of symmetry.
• $\overleftrightarrow{CE}$: $CE$ is the line connecting vertex $C$ to the mid - point $E$ of the opposite side $BA$, so it is a line of symmetry.
• $\overleftrightarrow{DE}$: $DE$ is not a line of symmetry as it does not connect a vertex to the mid - point of the opposite side.

Answer:

$\overleftrightarrow{BD}$, $\overleftrightarrow{AF}$, $\overleftrightarrow{CE}$