Transcript Notes 66: (10.3) Apply Properties of Chords

Notes 66: (10.3) Apply
Properties of Chords
THEOREM 10.3
• In the same circle, or in congruent circle, two minor arcs
are congruent if and only if their corresponding chords are
congruent.
𝐴𝐵 ≅ 𝐶𝐷 if and only if 𝐴𝐵 ≅ 𝐶𝐷.
THEOREM 10.4
• If one chord is a perpendicular bisector of another chord,
then the first chord is a diameter.
• If 𝑄𝑆 is a perpendicular bisector of 𝑇𝑅 ,
then 𝑄𝑆 is a diameter of the circle
THEOREM 10.5
• If a diameter of a circle is perpendicular to a chord, then
the diameter bisects the chord and its arc.
• If 𝐸𝐺 is a diameter and 𝐸𝐺 ⊥ 𝐷𝐹,
then 𝐻𝐷 = 𝐻𝐹, and 𝐺𝐷 ≅ 𝐺𝐹.
THEOREM 10.6
• In the same circle, or in congruent circles, two chords are
congruent if and only if they are equidistant from and only
the center.
• 𝐴𝐵 ≅ 𝐶𝐷 if and only if EF = EG.
Use congruent chords to find an arc
measure
• In the diagram, A  D, 𝐵𝐶 = 𝐸𝐹, and m𝐸𝐹 = 125.
Find m𝐵𝐶.
Use the diagram of E to find the length
of 𝑩𝑫. Tell what theorem you use.
In the diagram of F, AB = CD = 12.
Find 𝑬𝑭.
Independent Practice 1
• If m𝑇𝑉 = 121°, find m 𝑅𝑆.
Independent Practice 2
• Find the measures of:
• 𝐶𝐵
• 𝐵𝐸
• 𝐶𝐸
Independent Practice 3
• If AB = 27 and EF = GF = 7. Find CD.