Mathematics
In a right angled triangle, prove that the hypotenuse is the longest side.
Triangles
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Answer
Let LMN be a right angled triangle, ∠M = 90°
We know that,
Sum of angles of triangle = 180°
∴ ∠L + ∠M + ∠N = 180°
⇒ ∠L + 90° + ∠N = 180°
⇒ ∠L + ∠N = 180° - 90°
⇒ ∠L + ∠N = 90°
∴ ∠M > ∠L and ∠M > ∠N.
We know that, side opposite to the greatest angle is longest side.
∴ Hypotenuse LN, is the longest side of the triangle.
Hence, proved that hypotenuse is the longest side of the right angled triangle.
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Related Questions
In a △LMN, if ∠M = 90°, name the longest side of the triangle.
In the given figure, side AB of △ABC is produced to D such that BD = BC. If ∠A = 60° and ∠B = 50°, prove that :
(i) AD > CD
(ii) AD > AC
In the given figure, AB > AC. If BO and CO are the bisectors of ∠B and ∠C respectively, prove that BO > CO.
In the given figure, sides AB and AC of △ABC have been produced to D and E respectively. If ∠CBD = x° and ∠BCE = y° such that x > y, show that AB > AC.
