Understanding Congruent Chords in Circles: Properties and Theorems
This lesson explores the properties of congruent chords in a circle, focusing on Theorems 77 and 78. Theorems state that if two chords are equidistant from the center, they are congruent, and vice versa. Through examples and calculations involving Circle O and congruent chords AB and CD, we find the lengths of segments OP and OQ. Understanding these theorems helps in solving various geometric problems involving circles.
Understanding Congruent Chords in Circles: Properties and Theorems
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Presentation Transcript
Lesson 10.2 Congruent Chords
If two chords are the same distance from the center of a circle, what can we conclude? Theorem 77: If two chords of a circle are equidistant from the center, then they are congruent.
Theorem 78: If two chords of a circle are congruent, then they are equidistant from the center of the circle.
Given: Circle O, AB CD, OP = 12x – 5, OQ = 4x + 19 Find: OP Since AB CD, OP = OQ 12x – 5 = 4x + 19 x = 3 Thus, OP = 12(3) – 5 = 31
Given • Given • An isosceles Δ has two sides. • If 2 chords of a circle are , then they are equidistant from the center. • A Δwith two sides is isosceles. • Circle P, PQ AB, PR CB • ΔABC is isosceles, with base AC. • AB BC • PQ PR • ΔPQR is isosceles
