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Circle Segments and Volume: Understanding Chords, Arcs, and Congruence in Geometry

This review focuses on circle segments, including properties of congruent chords and their respective arcs. If two chords are congruent, their arcs are also congruent. The lesson involves solving equations for unknown variables, applying the Pythagorean Theorem where necessary, and exploring the relationships between diameters, chords, and circles. Practice problems from the workbook provide opportunities to apply these concepts, including finding lengths of segments within circles and using congruence properties to solve for missing values.

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Circle Segments and Volume: Understanding Chords, Arcs, and Congruence in Geometry

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  1. Find the Area

  2. EOCT Review Question of the Day

  3. Unit 3B Circle Segments and Volume

  4. If two chords are congruent, then their corresponding arcs are congruent.

  5. Solve for x. 8x – 7 3x + 3 8x – 7 = 3x + 3 x = 2

  6. Example Find WX.

  7. Example Find 130º

  8. If two chords are congruent, then they are equidistant from the center.

  9. In K, K is the midpoint of RE. If TY = -3x + 56 and US = 4x, find the length of TY. U T K E x = 8 R S Y TY = 32

  10. If a diameter is perpendicular to a chord, then it also bisects the chord.This results in congruent arcs too.Sometimes, this creates a right triangle & you’ll use Pythagorean Theorem.

  11. IN Q, KL  LZ. If CK = 2x + 3 and CZ = 4x, find x. x = 1.5 Q C Z K L

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

  13. Example 30 CE =

  14. Example LN = 96

  15. Practice • Workbook Page 211 and 212

  16. Segment Lengths in Circles

  17. Two chords intersect INSIDE the circle Type 1: part part part part Go down the chord and multiply

  18. Solve for x. 9 6 x 2 x = 3

  19. 12 2x 8 3x Find the length of DB. A D x = 4 C DB = 20 B

  20. Find the length of AC and DB. D A x – 4 x C 5 10 x = 8 AC = 13 DB = 14 B

  21. Practice WS Round to 3 decimal places Beware: HW ahead

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