1. ## Proof Help

Please solve this in a proof format ex: Statments | Reasons

2. ## Re: Proof Help

$\displaystyle \Delta ABX \sim \Delta DCX \Rightarrow$

$\displaystyle \Rightarrow |BX| : |BA| = |DX| : |DC| \Rightarrow$

$\displaystyle \Rightarrow |BX| \cdot |DC| = |BA| \cdot |DX|$

3. ## Re: Proof Help

Originally Posted by princeps
$\displaystyle \Delta ABX \sim \Delta DCX \Rightarrow$

$\displaystyle \Rightarrow |BX| : |BA| = |DX| : |DC| \Rightarrow$

$\displaystyle \Rightarrow |BX| \cdot |DC| = |BA| \cdot |DX|$
thanks but thats only half the proof, i need the reasons

4. ## Re: Proof Help

Originally Posted by Proclivitas
thanks but thats only half the proof, i need the reasons
Triangles ABX and DCX are similar because they have same angles...

5. ## Re: Proof Help

Hello, Proclivitas!

$\displaystyle \begin{array}{cccccc}1. & \angle B = \angle D && 1. & \text{Given} \\ 2. & \angle BXA = \angle DXC && 2. & \text{Vertical angles} \\ 3. & \Delta BXA \sim \Delta DXC && 3. & a.a.a. \\ 4. & \frac{BX}{BA} = \frac{DX}{DC} && 4. & \text{Proportions} \\ 5. & BX\cdot DC = BA\cdot DX && 5. & \text{Muliply by }BA\cdot DC \end{array}$