Given: △ABC, D ∈ ray BC
C∈ BD , AB=AC=BC
Prove: BD>DA>AB

BD>DA>AB because of the triangle inequality

Step-by-step explanation:

Triangle ABC is equilateral because AB=BC=AC (all the sides are equal)

So, m∠A=m∠B=m∠C=60° because its an equilateral triangle

m∠BAC and m∠CAD are complimentary so, m∠CAD is 30°

m∠ACD is 120° because of supplementary angles (30+m∠ACD=180;m∠ACD=120)

m∠ADC is also 30° (180-(30+120)=30)

The Triangle Inequality Theorem says: If two sides of a triangle are unequal, then the measures of the angles opposite these sides are unequal, and the greater angle is opposite, the greater side.

So, we know that 90 (m∠A)> 60 (m∠B)> 30 (m∠D)

So, if that's true then  BD>DA>AB because of the triangle inequality.

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step-by-step explanation: