RHS — Definition, Formula & Examples
RHS stands for Right-Hand Side, meaning everything on the right side of an equals sign or inequality. In geometry, RHS also refers to a triangle congruence rule for right triangles (Right angle–Hypotenuse–Side).
In an equation , the RHS is the expression . In Euclidean geometry, the RHS congruence criterion states that two right triangles are congruent if their hypotenuses and one pair of corresponding legs are equal in length.
How It Works
When you see an equation like , the RHS is and the LHS (Left-Hand Side) is . Textbooks use "RHS" and "LHS" as shorthand when describing steps in a proof or solution, such as "subtract 5 from both the LHS and RHS." In geometry, the RHS congruence test applies only to right triangles: if two right triangles share the same hypotenuse length and one matching leg, they are congruent.
Worked Example
Problem: Solve 2x + 3 = 11. Identify the LHS and RHS, then find x.
Identify sides: The LHS is 2x + 3. The RHS is 11.
Subtract 3 from both sides: Subtract 3 from the LHS and the RHS to keep the equation balanced.
Divide both sides by 2: Divide the LHS and RHS by 2.
Answer: x = 4. Throughout the solution, "RHS" referred to the right side of the equation.
Why It Matters
You will encounter the abbreviation RHS constantly in algebra textbooks, proofs, and exam mark schemes. Knowing this shorthand lets you follow worked solutions without confusion, especially in standardized tests where instructions say things like "show that the LHS equals the RHS."
Common Mistakes
Mistake: Confusing the geometry meaning of RHS (Right angle–Hypotenuse–Side congruence) with the general algebra meaning (Right-Hand Side).
Correction: Context tells you which meaning applies. In a triangle congruence problem, RHS is a congruence criterion. In an equation or proof, RHS means the right side of the equals sign.