how can i prove (s-b)/r = r(lowercase a)=(s-c)?
To prove that (s-b)/r = r * a = (s-c), where s, b, c, and r are given values, you'll need to use the properties of a triangle, specifically the fact that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Here is the step-by-step process to prove the equality:
1. Start with the given equation: (s - b)/r = r * a = (s - c).
2. Multiply both sides of the equation by r to eliminate the denominator:
(s - b) = r * r * a = r^2 * a = (s - c).
3. Rearrange the terms to isolate the values:
(s - b) - (s - c) = r^2 * a.
4. Simplify the equation by combining like terms:
s - b - s + c = r^2 * a.
5. The s terms cancel out, leading to:
-b + c = r^2 * a.
6. Add b to both sides of the equation:
-b + c + b = r^2 * a + b.
7. The -b and b terms cancel out, yielding:
c = r^2 * a + b.
8. Finally, subtract the term r^2 * a from both sides of the equation:
c - r^2 * a = b.
Therefore, the equation is proven to be true.