Question

Show that in a right angled traingle,the hypotenuse is the largest side.

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Answer 1

Given:

• ABC is a triangle right angled at B.

Need to prove:

• The hypotenuse is the largest side.

Proof:

In ∆ ABC,

<A + <B + <C = 180° [ sum of interior angles of a ∆]

<A + 90° + <C = 180°

<A + <C = 90°

So, <A and <C must be less than 90° and <B is 90°.

Since, the side opposite to largest angle is the largest.

Therefore,

AC is the hypotenuse which is the largest side of the right angles traingle ABC.

Answer 2

$\huge \underline \mathbb {SOLUTION:-}$

Given:

• ∆ ABC is a right angled-triangle
• Right angled at B i.e. ∠ B = 90°

To Prove:

• AC is the longest side of ∆ ABC

Proof:

In ∆ABC,

∠A + ∠B + ∠C = 180° (Angle sum property of triangle.)

∠A + 90° + ∠C = 180° (Given ∠B = 90°)

∠A + ∠C = 180° - 90°

∠A + ∠C = 90°

Angle can't be 0 or negative.

Hence:

∠A < 90°

∠A < ∠B

BC < AC (Side opposite to the greater angle is longer)

Also:

∠C < 90°

∠C < ∠B

AB < AC (Side opposite to the greater angle is longer)

Therefore:

• AC is longest side in ∆ABC

❝Hence Proved❞

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