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build BCBC=ACCBA=A=aBCE=2aBC=BEE=BCE=2aEBF=E+A=3aq.e.d
Join BC. Then AC = BC = BE. β = α + ∠BEA= α + ∠BCE= α + α + ∠CBA= α + α + α= 3α
Draw a line from point B to C. Triangle ABC is an isosceles triangle, AC = BC, then ∠CAB = ∠CBA.∠BCE = 2α.in triangle ABE if ∠AEB is x then ∠EBF is exterior angle, then β = α + x∠BCE = ∠AEB = 2α then β = α + 2α = 3α (q.e.d)
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build BC
ReplyDeleteBC=AC
CBA=A=a
BCE=2a
BC=BE
E=BCE=2a
EBF=E+A=3a
q.e.d
Join BC. Then AC = BC = BE.
ReplyDeleteβ = α + ∠BEA
= α + ∠BCE
= α + α + ∠CBA
= α + α + α
= 3α
Draw a line from point B to C.
ReplyDeleteTriangle ABC is an isosceles triangle, AC = BC, then ∠CAB = ∠CBA.
∠BCE = 2α.
in triangle ABE if ∠AEB is x then ∠EBF is exterior angle, then β = α + x
∠BCE = ∠AEB = 2α then β = α + 2α = 3α (q.e.d)