Lesson 4 intersecting chords and their propertes
- 1. Lesson 4: Intersecting Chords and Their Properties 4.1: Intersecting Chords Theorem 4.2: Angles of Intersecting Chords Theorem
- 2. 4.1: Intersecting Chords Theorem If two chords of a circle intersect inside the circle, then the product of the measures of the segments of one chord is equal to the product of the measures of the segments of the other chord.
- 4. Theorem 4.2: Angles of Intersecting Chords Theorem If two chords of the same circle intersect, then the total measure of a pair of vertical angles is equal to the total measure of the arcs intercepted by these angles.
- 5. Why ∠KLM instead of ∠KLN which is asked originally? Because getting the ∠KLM will lead us to get the ∠KLN from the absolute concept that the total measure of all the angles within the circle created by the intersecting chords which are the ∠KLM, ∠OLN, ∠MLO and ∠KLN is 360⁰. Thus, ∠KLM + ∠OLN + ∠MLO + ∠KLN =360⁰ and according to VERTICAL ANGLE THEOREM, m∠KLM = m∠OLN and m∠MLO = m∠KLN We can therefore take m∠KLM to represent its corresponding vertical angle m∠OLN, and make it 2(m∠KLM) for two of them. We can also take m∠KLN to represent its corresponding vertical angle m∠MLO and make it 2(m∠KLN) for two of them. Thus, we can have 2(m∠KLM) + 2(m∠KLN) =360⁰
- 6. Thus, 2(m∠KLM) = 120⁰ m∠KLM = 120/2 = 60⁰
- 7. STEP 2: 2(m∠KLM) + 2(m∠KLN) = 360 2(60 ) + 2(m∠KLN) = 360 120 + 2(m∠KLN)=360 2(m∠KLN) = 360-120 2(m∠KLN) = 240 m∠KLN = 240/2 thus we got final answer m∠KLN= 120
- 8. 3 points each item. Only answers showing complete process of solution will get 3 points. Correct processes with wrong final answers still will get 1 to 2 points. Activity: