Side bc of triangle abc is produced to d
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the side of BC of triangle ABC is produced to D If the bisector of angle A meets BC in L. prove that angle abc + angle acd = 2 angle ALC
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Answer:
∠ABC + ∠ACD = 2∠ALC
Step-by-step explanation:
the side of BC of triangle ABC is produced to D If the bisector of angle A meets BC in L. prove that angle abc + angle acd = 2 angle ALC
the bisector of angle A meets BC in L
=> ∠BAL = ∠CAL = x
Let say ∠ABC = ∠ABL = α ( as L is on BC)
∠ALC = ∠ABL + ∠BAL
=> ∠ALC = α + x
∠ACD = ∠ALC + ∠CAL
=> ∠ACD = α + x + x
∠ABC + ∠ACD = α + α + x + x
=> ∠ABC + ∠ACD = 2 ( α + x)
=> ∠ABC + ∠ACD = 2∠ALC
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