Question

Show that in right angled triangle the hypotenuse is the longest side?

Answer 1

In a right angled triangle, the angle opposite To the hypotenuse is 90°, while other two angles are Always less than 90°. As you know that the side opposite to the largest angle is always the largest in a triangle.

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Answer 2

Answer:

$\huge\sf{\underline{\underline{Given :-}}}$

A triangle ABC in which ∠ABC = 90°.

$\huge\sf{\underline{\underline{To\:\:Prove :-}}}$

• AC > AB
• AC > BC

$\huge\sf{\underline{\underline{Proof :-}}}$

In ∆ ABC = 90°

But,

∠ ABC + ∠ BCA + ∠ CAB = 180°

$\therefore$ 90° + ∠ BCA + ∠ CBA = 180°

=> ∠ BCA + ∠ CBA = 90°

• ∠ BCA and ∠ CBA are acute angle.
• ∠ BCA < 90° and ∠ CBA < 90°
• ∠ BCA < ∠ ABC and ∠ CAB < ∠ ABC .
• AC > AB and AC > BC .