Question

show that in a 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.

Answer 2

$\huge\underline\mathfrak\red{Answer:}$

Let ABC be an isosceles triangle with AB = AC.

Draw the bisector AD of $\angle$A which meets BC in D.

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In ∆ABD and ∆ACD, we have

• AB = AC
• $\angle$BAD = $\angle$CAD
• AD = AD

1st was given

2nd was (AD is bisector of $\angle$A)

3nd was common.

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So, by SAS-CRITERION of congruence, we have

∆ABD $\cong$ ∆ACD.

$\implies$ $\angle$C = $\angle$B.

The converse of the above is true i.e., if two angles of a triangle are equal, then the opposite to them are also equal.