Learning Task 3: In your answer sheet, copy and answer.
KL KM
Given: and
are tangent and
secant segments, respectively,
of 00 drawn from exterior point K.
K
N
KM
intersects OO at N.
Prove: (KL)2 = KM KN
LM LN
Draw and so that we formed two similar triangles. Then show the
proof using the Two Column Proof.
Proof:
Statement
Reason
m2NLK =
LN
(m ) and
(1)
>
1
LN
mZLMN (m
m2NLK = m_LMN
(2)
(3)
NLK LLMN
m LNK = m NLM + m2LMN
mZLNK = m NLM + m2NLK
(4)
(5)
(6)
m KLM = m_NLM + m2NLK
m2LNK = m KLM
(7)
LLNK
LKLM
(8)
~ALNM
MKL
(9)
КМ
10. Lengths of sides of similar triangles are
İLK!
KM KN
PIVOT 4A CALABARZON Math GIO
(10)
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