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- ⟨BAC = 90°
GIVEN :-
- “AD” perpendicular to “BC” .
- (AD)² = (BD) × (DC)
CALCULATION :-
In ∆ADB,
- (AB)² = (AD)² + (BD)² -----(1)
In ∆ADC,
- (AC)² = (AD)² + (DC)² -------(2)
☞ Adding Equation (1) and Equation (2), we get
(AB)² + (AC)² = 2(AD)² + (BD)² + (DC)²
=> (AB)² + (AC)² = 2(BD × CD) + (BD)² + (DC)²
=> (AB)² + (AC)² = (BD + CD)²
=> (AB)² + (AC)² = (BC)²
☞ So, here ∆ABC is a right angled triangle where angle (BAC) = 90° .
♻️ Hence, Proved .
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hope this helps you mate ✨
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