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# 2 Isosceles Triangles Question

ABC and DAC are two isosceles triangles with angle BAC = 20 and angle ADC = 100. Show that AB = BC + CD.

Note by Mithil Shah
4 months, 3 weeks ago

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Construct DE such that E lies on AB and angle ADC=60°. Then; ADE will be an equilateral triangle.
Then; AE=ED=DA ;
But; DA=DC
So; AE=DC............... (1)

Next; we can join EC and by some elementary angle chasing we can conclude angle BEC= angle BCE and hence;
BE=BC................ (2)

Adding (1) & (2) gives the desired result i.e. AE+BE=BC+DC or AB=BC+CD. · 4 months, 3 weeks ago

AB=AC and DA=DC · 4 months, 3 weeks ago

you haven't specified which sides are equal in these isosceles triangles · 4 months, 3 weeks ago