Question

Prove AD= 3AB show exact steps to solve use algebraic terms for each step " Distributive property or Associative Multiplicative property" as of that

Answer 1

The question is to prove that

$AD=3AB$

From the diagram in the question, we can deduce that

$AD=AB+BC+CD\text{ (TOTAL DIsTANCE FOR THE LINE)}$

Also given from the question, we have

B is the midpoint of AC, that is

$AB=BC(\text{ B bisects AC into two equal parts)}$

Also given from the question, we have

C is the midpoint of BD, that is

$BC=CD\text{ ( C bisects BD into two equal parts)}$

Therefore,

since BC=CD ,and BC=AB then,

$CD=AB\text{ (THE LINE IS DIVIDED INTO EQUAL SEGMENTS)}$

By substituting the values of BC and CD in the total distance for the line , we will have

$\begin{gathered} AD=AB+BC+CD \\ AD=AB+AB+AB \\ AD=3AB\text{ (AD IS 3 times the length of AB because the line is divided into equal lengths)} \\ \text{PROVED} \end{gathered}$