Show that in a right angled triangle,the hypotenuse is the longest side - Maths - Triangles

Question

Show that in a right angled triangle,the hypotenuse is the
longest side

Priyanka Kedia · Accepted Answer

$L e t A B C b e a r i g h t t r i a n g l e r i g h t a n g l e d a t C . T o \Pr o v e : H y p o t e n u s e A B i s t h e l o n g e s t s i d e . i . e ., A B > A C a n d A B > B C \Pr o o f : I n Δ A B C, ∠ A C B = 90^{0} ∠ A C B + ∠ C B A + ∠ B A C = 180^{0} \Rightarrow 90^{0} + ∠ C B A + ∠ B A C = 180^{0} \Rightarrow ∠ C B A + ∠ B A C = 180^{0} - 90^{0} \Rightarrow ∠ C B A + ∠ B A C = 90^{0} \Rightarrow ∠ C B A a n d ∠ B A C a r e a c u t e a n g l e s . \Rightarrow ∠ C B A < 90^{0} a n d ∠ B A C < 90^{0} \Rightarrow ∠ C B A < ∠ A C B a n d ∠ B A C < ∠ A C B \Rightarrow A B > A C a n d A B > B C (s i d e o p p o s i t e t o g r e a t e r a n g l e is l \arg e r)$

Show that in a right angled triangle,the hypotenuse is the longest side.