CPM Homework Help : CCG Problem 8-118

A circle with center, C, diameter, E D, & radii, A C, & B C, has chord A B, intersecting radius C E, at point, F. Larry started to set up a proof to show that if $\overline{AB} \bot \overline{DE}$ and $\overline{DE}$ is a diameter of $\odot C$ , then $\overline{AF} \cong \overline{FB}$ . Examine his work below. Then complete his missing statements and reasons.

Statements	Reasons
$\overline{AB} \bot \overline{DE}$ and is a diameter of $\odot C$ .
$\angle AFC$ and $\angle BFC$ are right angles.
$FC = FC$
$AC = BC$	Definition of a Circle (radii must be equal)
	$\text{HL}\cong$
$\overline{AF}\cong\overline{FB}$

Hint:

Click the check boxes as they appear in order to complete the proof.

Reason 1:

Reason 2:

Reason 3:

1. Given

2. Definition of perpendicular

3. Reflexive property

Statement 5:

Reason 6:

5. $\Delta AFC \cong \Delta BFC$

6. $\cong \Delta \rightarrow \: \cong \text { parts}$