Question

Prove that in a right angle triangle hypotenuse is the longest side

Answer 1

side opposite to greater side is greatest

Answer 2

Step-by-step explanation:

Given:

• A right angled triangle.

To Prove:

• Hypotenuse is the longest side in right angles triangle.

Solution: Let ABC be a right angled triangle win which ∠B = 90°

• We know that the sum of all three angles of a triangle is of 180° •

→ ∠A + ∠B + ∠C = 180°

→ ∠A + 90° + ∠C = 180°

→ ∠A + ∠C = 180° – 90°

→ ∠A + ∠C = 90°

Since, ∠A + ∠C = 90°

∴ ∠B > ∠A and ∠B > ∠C

=> AC > BC and AC > AB [ side opposite to larger angle is longer ]

∴ AC is the longest side.

Hence, In a right triangle, the hypotenuse is the longest side.