Question

A- CE=CD B- CE = CA C- BF=DF D- DF=EF please help!!

Answer 1

The perpendicular bisector theorem gives the statements that ensures

that $\overleftrightarrow{FG}$ and $\overleftrightarrow{AB}$ are perpendicular.

The two statements if true that guarantee  $\overleftrightarrow{FG}$ is perpendicular to line $\overleftrightarrow{AB}$ are;

• $\overline{CE} = \overline{CD}$

• $\overline{DF} = \overline{EF}$

Reasons:

The given diagram is the construction of the line $\mathbf{\overleftrightarrow{FG}}$ perpendicular to line $\mathbf{\overleftrightarrow{AB}}$.

Required:

The two statements that guarantee that  $\overleftrightarrow{FG}$ is perpendicular to line $\overleftrightarrow{AB}$.

Solution:

From the point C arcs E and D are drawn to cross line $\overleftrightarrow{AB}$, therefore;

$\overline{CE} = \mathbf{\overline{CD}}$ arcs drawn from the same radius.

$\overleftrightarrow{FG}$ is perpendicular to line $\overleftrightarrow{AB}$, given.

Therefore;

$\overline{DF} = \overline{EF}$  by perpendicular bisector theorem.

Learn more about the perpendicular bisector theorem here:

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