Question

In ∆LMN, m∠M = 40°, m∠N = 50°. Which of the following statements is true?


(1) [l (MN)]² = [l (LM)]² + [l (LN)]²
(2) [l (LM)]² = [l (MN)]² + [l (LN)]²
(3) [l (LN)]² = [l (LM)]² + [l (MN)]²

Answer 1

(1) [l (MN)]² = [l (LM)]² + [l (LN)]² is true.
We know that sum of the angles of a triangle is 180°
∴ $\angle$L + $\angle$M + $\angle$N = 180°
⇒ $\angle$L + 40° + 50° = 180°
⇒ $\angle$L + 90° = 180°
⇒ $\angle$L = 180° - 90°
⇒ $\angle$L = 90°
$\angle$L = 90°
∴ ∆LMN is a right-angled triangle.

∴ By Pythagoras theorem
(Hypotenuse)² = (side one)² + (side two)²
⇒ [l (MN)]² = [l (LM)]² + [l (LN)]²