Question

Corresponding parts enter the number that belongs in the green box

Answer 1

AB=6

Step-by-step explanation

Step 1

set the equations

due to lengths AD and DC are the same, and the distance DB is common for triangels ADB and DBC

we can state that

triiangles are similar,so

`AB=AC\Rightarrow equation(1)`

and

`\begin{gathered} AC=12 \\ AC=AB+BC \\ AB+BC=12\Rightarrow equation(2) \end{gathered}`

Step 2

solve for AB

a) replace the AB value from equation(1) into equation(2)

`\begin{gathered} AB+BC=12\Rightarrow equation(2) \\ AB+AB=12 \\ \text{add like terms} \\ 2(AB)=12 \\ \text{divide both sides by 2} \\ (2(AB))/(2)=(12)/(2) \\ AB=6 \end{gathered}`

therefore, the answer is

AB=6

I hope this helps you