Answer:
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.
