1. ## geometry

plz help

a, b, c, and d are real numbers and a > c, b> d, a/b = c/d = r
Prove that a-c / b-d = r

2. Originally Posted by jenjen
plz help

a, b, c, and d are real numbers and a > c, b> d, a/b = c/d = r
Prove that a-c / b-d = r
Please use parenthesis. What you wrote is
$\displaystyle a - \frac{c}{b} - d$

To write it as you intended write (a - c)/(b - d) = r.

$\displaystyle \frac{a}{b} = r$ means that $\displaystyle a = br$

$\displaystyle \frac{c}{d} = r$ means that $\displaystyle c = dr$

So
$\displaystyle \frac{a - c}{b - d} = \frac{br - dr}{b - d} = \frac{r(b - d)}{b - d} = r$

-Dan

3. Hello, jenjen!

What have you tried?
. . It's fairly straight-forward.

$\displaystyle a,\,b,\,c,\,d$ are real numbers, and: .$\displaystyle a > c,\;\;b> d,\;\;\frac{a}{b}\,=\,\frac{c}{d}\,= \,r$

Prove that: .$\displaystyle \frac{a-c}{b-d}\:=\:r$
From $\displaystyle \frac{a}{b} \:=\:r$, we have: .$\displaystyle a \:=\:br$ .[1]

From $\displaystyle \frac{c}{d} \:=\:r$, we have: .$\displaystyle c \:=\:dr$ .[2]

Subtract [2] from [1]: .$\displaystyle a - c \:=\:br - dr\quad\Rightarrow\quad a-c\:=\:(b-d)r$

Therefore: .$\displaystyle \frac{a - c}{b-d} \:=\:r$

4. To Topsquark:

Hi, thank you so much Topsquark. You save my life!

To Soroban: I agreed with you. It is straightforward but then sometimes I can't see through simple problems. I often make math problems more complicated than it is and fool myself.