### Home > INT2 > Chapter 8 > Lesson 8.4.1 > Problem8-85

8-85.

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

 Statements Reasons 1. $\overline{AB} ⊥ \overline{DE}$ and $\overline{DE}$ is a diameter of ⊙$C$. 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.

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

1. Given

2. Definition of perpendicular

3. Reflexive Property

5. $ΔAFC≅ΔBFC$

6. $≅ Δ → ≅$ parts