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.

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !

i’m here for points.