(5) ∠OGD ≅∠AHF=90° //(2), (4), definition of perpendicular lines (4) AB⊥EF // A diameter that bisects a chord is perpendicular to that chord (2) AB⊥CD // A diameter that bisects a chord is perpendicular to that chord Here's how you prove that if a diameter bisects two chords, they are parallel to each other: We'll prove this using each of the three.
any of these three methods will work, and all are as easy to show.
Since we have shown that the diameter that bisects a chord is perpendicular to that chord. To show two lines are parallel, we can use one of the several methods: either show congruent corresponding angles, congruent alternating interior angles, or the Perpendicular Transversal Theorem. Show that the chords are parallel to each other. In circle O, AB is a diameter that bisects two chords, CD and EF. We can do this this three ways, relying on the properties of parallel and perpendicular lines. In today's geometry lesson, we will prove that if a diameter bisects two chords in a circle, the two chords are parallel to each other.
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