CPM Homework Help : INT2 Problem 8-85

A circle can be named by its center, as in circle $C$ , or $\odot C$ at right. Larry started to set up a proof to show that if $\overline{AB} ⊥ \overline{DE}$ and $\overline{DE}$ is a diameter of $\odot C$ , then $\overline{AF} ≅ \overline{FB}$ . Examine his work below. Then complete his missing statements and reasons.

Statements	Reasons
1. $\overline{AB} ⊥ \overline{DE}$ and $\overline{DE}$ is a diameter of $\odot C$ .	1.
2. $∠AFC$ and $∠BFC$ are right angles.	2.
3. $\overline{FC} ≅ \overline{FC}$	3.
4. $\overline{AC} ≅ \overline{BC}$	4. Definition of a circle (radii must be equal)
5.	5. $HL ≅$
6. $\overline{AF} ≅ \overline{FB}$	6.

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. $ΔAFC≅ΔBFC$

6. $≅ Δ → ≅$ parts