Mrs.D Math · 8th Grade

RIGHT
VERDICT

Converse of the Pythagorean Theorem
📐 Pythagorean Theorem
📏 Hypotenuse & Legs
⚖️ a² + b² = c²
✅ 3-4-5 → Right!
🔍 Does a²+b²=c²?
❌ 4-5-6 → Not Right
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⚖️ The Converse of the Pythagorean Theorem

The Big Idea

If a² + b² = c², then the triangle IS a right triangle.

The sides are the evidence. Test them with the formula and deliver your verdict!

1
Find c — the LONGEST side is always the hypotenuse candidate.
Sides 6, 10, 8 → c = 10, legs = 6 and 8
2
Square the two shorter sides and add: a² + b²
6² + 8² = 36 + 64 = 100
3
Compare with c². Equal → RIGHT triangle ✅. Not equal → NOT right ❌
10² = 100 → 100 = 100 → Right triangle!

Why the Real World Cares

Builders can't "eyeball" a right angle — but they CAN measure sides! Measure two edges and the diagonal, then test with a² + b² = c².

✓
A 3 ft × 4 ft gate with a 5 ft diagonal: 9 + 16 = 25 → the corner is square ✅
✗
A 3 ft × 4 ft gate with a 6 ft diagonal: 9 + 16 ≠ 36 → the corner is crooked ❌

How to Play

📐
Is It Right? — Test three side lengths. Choose the verdict WITH the correct reasoning.
🏗️
Real World — Gates, ramps, ladders, and frames. Do the measurements prove a right angle?
🎲
Mixed — Both types together for the ultimate case load!
🧮
Calculator — Tap the gold calculator button any time. Try it in your head first — then verify!
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IS IT RIGHT?
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