11 3 arcs and chords lesson
- 1. Arcs and ChordsArcs and Chords You will learn to identify and use the relationships among arcs, chords, and diameters. Nothing New!
- 2. Arcs and ChordsArcs and Chords BD S C P A In circle P, each chord joins two points on a circle. Between the two points, an arc forms along the circle. vertical angles By Theorem 11-3, AD and BC are congruent because their corresponding central angles are _____________, and therefore congruent. By the SAS Theorem, it could be shown that ΔAPD ΔCPB. Therefore, AD and BC are _________.congruent The following theorem describes the relationship between two congruent minor arcs and their corresponding chords.
- 3. Arcs and ChordsArcs and Chords Theorem 11-4 In a circle or in congruent circles, two minor arcs are congruent if and only if (iff) their corresponding ______ are congruent. B D C A chords AD BC iff AD BC
- 4. Arcs and ChordsArcs and Chords A BC The vertices of isosceles triangle ABC are located on R. R If BA AC, identify all congruent arcs. BA AC
- 5. Arcs and ChordsArcs and Chords Step 1) Use a compass to draw circle on a piece of patty paper. Label the center P. Draw a chord that is not a diameter. Label it EF. Step 2) Fold the paper through P so that E and F coincide. Label this fold as diameter GH. E F P G H Q1: When the paper is folded, how do the lengths of EG and FG compare? Q2: When the paper is folded, how do the lengths of EH and FH compare? Q3: What is the relationship between diameter GH and chord EF? EG FG EG FG They appear to be perpendicular.
- 6. Arcs and ChordsArcs and Chords Theorem 11-5 In a circle, a diameter bisects a chord and its arc if and only if (iff) it is perpendicular to the chord. P R D C B A AR BR and AD BD iff CD AB Like an angle, an arc can be bisected.
- 7. Arcs and ChordsArcs and Chords B C A K D 7 Find the measure of AB in K. AB=2(DB) Theorem 11-5 AB=2(7) AB=14 Substitution
- 8. Arcs and ChordsArcs and Chords M K L K N6 Find the measure of KM in K if ML = 16. (KM )2 =(KN )2 +(MN)2 Pythagorean Theorem (KM )2 =(6)2 +(8)2 Given; Theorem 11-5 (KM )2 =36+64 (KM )2 =100 √(KM)2 =√100 KM=10