Question

plz ans with process​

Answer 1

$\large\underline{\bold{Solution :- }}$

We know,

• In a triangle, sum of any two sides of a triangle is always greater than third side.

So,

$\rm :\longmapsto\:In \: \triangle \: OXY$

$\rm :\implies\: \boxed{ \bf \: OX \: + \: OY \: > \: XY} - - (1)$

$\rm :\longmapsto\:In \: \triangle \: OXZ$

$\rm :\implies\: \boxed{ \bf \: OX \: + \: OZ \: > \: XZ} - - (2)$

$\rm :\longmapsto\:In \: \triangle \: OYZ$

$\rm :\implies\: \boxed{ \bf \: OY \: + \: OZ \: > \: YZ} - - (3)$

So,

• On adding equation (1), (2) and (3), we get

$\bf :\implies\:2(OX + OY + OZ) > XY + YZ + XZ$

$\large{\boxed{\bf{Hence, Proved}}}$

Properties of a triangle

• A triangle has three sides, three angles, and three vertices.

• The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.

• The sum of the length of any two sides of a triangle is greater than the length of the third side.

• The side opposite to the largest angle of a triangle is the largest side.

• Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.

Based on the angle measurement, there are three types of triangles:

• Acute Angled Triangle : A triangle that has all three angles less than 90° is an acute angle triangle.

• Right-Angled Triangle : A triangle that has one angle that measures exactly 90° is a right-angle triangle.

• Obtuse Angled Triangle : triangle that has one angle that measures more than 90° is an obtuse angle triangle.