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Math II

In this lesson, we explore the special properties of circles, focusing on the relationships between angles, arcs, and chords. We learn how to use angle measures to determine the lengths of arcs, and discover that two minor arcs are congruent if their corresponding chords are also congruent. We'll investigate the significance of diameters, particularly how a diameter that is perpendicular to a chord bisects both the chord and its associated arc. Examples and practice problems will reinforce these concepts.

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Math II

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  1. Math II UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MM2G1, MM2G2 Today’s Question: How do we use angle measures to find measures of arcs? Standard: MM2G3.a,d

  2. Arcs and Section 6.2, 6.3 Chords

  3. In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. B C AB  CD IFF AB  DC A D

  4. 60 120 120 x x = 60

  5. 2x x + 40 2x = x + 40 x = 40

  6. What can you tell me about segment AC if you know it is the perpendicular bisectors of segments DB? D It’s the DIAMETER!!! A C B

  7. Ex. 1 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. x = 24 24 y 60 y = 30 x

  8. Example 2 EX 2: In P, if PM  AT, PT = 10, and PM = 8, find AT. P A M MT = 6 T AT = 12

  9. Example 3 In R, XY = 30, RX = 17, and RZ  XY. Find RZ. X RZ = 8 R Z Y

  10. Example 4 IN Q, KL  LZ. IF CK = 2X + 3 and CZ = 4x, find x. Q x = 1.5 C Z K L

  11. In the same circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center. B AD  BC IFF LP  PM A M P L C D

  12. Ex. 5: InA, PR = 2x + 5 and QR = 3x –27. Find x. R A x = 32 Q P

  13. Ex. 6: IN K, K is the midpoint of RE. If TY = -3x + 56 and US = 4x, find x. U T K E R S x = 8 Y

  14. Homework: • Page 201 #7-12

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