if $ \overline { g o } \cong \overline { h o } $ and diameter $ \overline { e j } $ is perpendicular to both chords $ \overline { d f } $ and $ \overline { i k } $, what is the relationship between $ \overline { g f } $ and $ \overline { h k } $?
go and ho are $ \frac { } { } $ which means $ \frac { } { } $ df and ik are also $ \frac { } { } $ the diameter ej is perpendicular so it creates a $ \frac { } { } $ gf must also be $ \frac { } { } $ to hk
word bank:
similar radius congruent parallel bisector congruent chords congruent
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Question

Accepted Answer

# Answer:
Blank 1: congruent
Blank 2: chords
Blank 3: congruent
Blank 4: congruent

# Explanation:
## Step1: Identify the nature of $ \overline{GO} $ and $ \overline{HO} $
Since $ \overline{GO} \cong \overline{HO} $, they are congruent.
## Step2: Relate to chords $ \overline{DF} $ and $ \overline{IK} $
In a circle, if the distances from the center to two chords are equal (here $ GO = HO $ as they are congruent and $ EJ$ is the line from center $ O$ to chords $ DF$ and $ IK$), the chords $ DF$ and $ IK$ are congruent.
## Step3: Use the perpendicular diameter property
The diameter $ EJ$ is perpendicular to chords $ DF$ and $ IK$. By the perpendicular - bisector theorem for chords in a circle,  $ GF=\frac{1}{2}DF$ and $ HK = \frac{1}{2}IK$. Since $ DF\cong IK$, then $ GF\cong HK$.

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the nature of \( \overline{GO} \) and \( \overline{HO} \)

Step2: Relate to chords \( \overline{DF} \) and \( \overline{IK} \)

Step3: Use the perpendicular diameter property

Answer: