THEOREM — Connect the three squares

DISCOVER

Start with a sketch and a prediction.

In the dissection, which triangle side becomes the side of the combined square? State a relationship between the three square areas.

Try on paper first. Use the model to test your idea before accepting the explanation.

Understand

For a right triangle with perpendicular legs a and b and hypotenuse c, $a^2$ + $b^2$ = $c^2$. The hypotenuse is opposite the right angle. Conversely, if a triangle’s longest side c satisfies this equation, the opposite angle is right.

Key Ideas

$a^2$ + $b^2$ = $c^2$

Never use the theorem for a triangle merely because its drawing looks right-angled.

Visualise

Method

Establish the right angle and identify the hypotenuse before substituting. Add squared legs to find c; subtract the known leg’s square from $c^2$ to find the other leg. Take the positive square root.

Worked Example

AIMS Method

1. A — Attempt independently
   Sketch and predict before using a formula.
2. I — Investigate the idea
   Separate given facts from visual assumptions.
3. M — Make connections
   Connect area, length, algebra and geometric constructions.
4. S — Scrutinise your reasoning
   Check each hypothesis and justify the conclusion.

Think first. Use AI purposefully. Verify always.

Focused Practice

Check & Feedback

Textbook connection: Ganita Prakash · Grade 8 · Part II · Chapter 2 — The Baudhāyana–Pythagoras Theorem · printed page 46