The following figure shows a triangle ABC in which AB=AC, M is a point on AB and N is a point on AC such that BM=CN. Prove that : i) AM=AN ii) ΔAMC≅ΔANB iii) BN=CM iv) ΔBMC≅ΔCNB
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Solution
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i)
Since,
AB=AC &
BM=CN
⇒AM=AN [SS THEOREM]
ii)
Since,
AB=AC &
AM=AN
∠A=∠A
⇒△AMC≈△ANB[SAS THEOREM]
iii)
Since,
AB=AC
AM=AN
BM=CN
⇒BN=CM [SSS THEOREM]
iv)
Since,
BM=CN
MC=BN
BC=BC
⇒△BMC≈△CNB[SSS THEOREM]
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Q1
The following figure shows a triangle ABC in which AB=AC, M is a point on AB and N is a point on AC such that BM=CN. Prove that : i) AM=AN ii) ΔAMC≅ΔANB iii) BN=CM iv) ΔBMC≅ΔCNB
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