Question

rewrite the theorem using information from the image.

theorem: if two chords are congruent, then they are equidistant from the center.

if , then

Explanation:

Identify the hypothesis and conclusion from the image

The general theorem is: "If two chords are congruent, then they are equidistant from the center."
From the image:

• The center of the circle is \(A\).
• The two chords are \(EF\) and \(DC\).
• The distances from the center \(A\) to the chords are represented by the perpendicular segments \(AG\) and \(AH\).
• Therefore, the hypothesis "two chords are congruent" translates to \(EF \cong DC\) (or \(DC \cong EF\)).
• The conclusion "they are equidistant from the center" translates to \(AG = AH\) (or \(AG \cong AH\)).

Match the dropdown options

The standard representation for the conditional statement in geometry is:
If \(EF \cong DC\), then \(AG \cong AH\) (or \(AG = AH\)).

Answer:

Rewrite the theorem using information from the image.

Theorem: If two chords are congruent, then they are equidistant from the center.

If <blank>\(EF \cong DC\)</blank>, then <blank>\(AG \cong AH\)</blank>