Name each of the following triangles in two different ways: (you may judge the nature of the angle by observation)
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To do:

We have to name each of the given triangles in two different ways.

Solution:

A scalene triangle is a triangle in which all three sides are of different lengths, and all three angles are of different measures.

An isosceles right triangle is a right-angled triangle with an equal base and height.

An obtuse-angled triangle is a triangle in which one of the interior angles measures more than $90^o$.

A right triangle is a triangle in which one angle is a right angle.

An equilateral triangle is a triangle in which all three sides have the same length.

An acute-angled triangle is a triangle in which all three interior angles are less than $90^o$

An isosceles triangle is a triangle that has two sides of equal length.

 (a) All the angles in the triangle are less than $90^o$ and two sides are equal.

Therefore,

The given triangle is an isosceles triangle as well as an acute-angled triangle.

(b) One of the angles in the triangle is equal to $90^o$ and all the sides are of different lengths.

Therefore,

The given triangle is a right-angled triangle as well as a scalene triangle.

(c) One of the angles in the triangle is more than $90^o$ and two sides are equal.

Therefore,

The given triangle is an isosceles triangle as well as an obtuse-angled triangle.

(d) One of the angles in the triangle is equal to $90^o$ and two sides are equal.

Therefore,

The given triangle is a right-angled triangle as well as an isosceles triangle.

(e) All the angles in the triangle are less than $90^o$ and the three sides are equal.

Therefore,

The given triangle is an equilateral triangle as well as an acute-angled triangle.

(f) One of the angles in the triangle is more than $90^o$ and all the sides are of different lengths.

Therefore,

The given triangle is a scalene triangle as well as an obtuse-angled triangle.