grade 10 Math lesson

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: