AB and CD are two parallel chords of a circle whose diameter is AC. Prove that AB=CD
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given: AB and CD are two chords of the circle such that ABCD and AC is the diameter of the circle.
TPT: AB = CD
proof:
in the triangles CBA and ADC,
∠CBA = ∠ADC = 90 [angles in the semi circle]
∠BAC = ∠ACD [alternate interior angles]
AC is common.
therefore by AAS congruency, triangles are congruent.
thus AB = CD [CPCT]
hope this helps you.
TPT: AB = CD
proof:
in the triangles CBA and ADC,
∠CBA = ∠ADC = 90 [angles in the semi circle]
∠BAC = ∠ACD [alternate interior angles]
AC is common.
therefore by AAS congruency, triangles are congruent.
thus AB = CD [CPCT]
hope this helps you.
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