Triangles are enclosed shapes that have three sides. More specifically, they are polygon shapes with three edges and vertices and only three lines. They are pretty standard and are the most elementary shapes in geometry. Since triangles have three sides, they have three angles. All three angles of the triangle add up to 180 degrees.

The word 'Iso' originated from the Greek word 'Iso', which means same, and ‘Scles’ originated from the Greek word 'skeles', which means legs. So the isosceles triangle is a triangle with two equal sides and angles. The sides of the triangle that are identical to each other are known as the legs of the triangle, and the other side of the triangle that is not equal is known as the triangle’s base. Therefore, isosceles triangles contain two identical base angles. This is due to the similar lengths in the triangle's lines and one other angle. Thus, the angles formed by the isosceles triangles are also acute. These properties make it easier to distinguish the isosceles triangles from other triangles.

Various formulas calculate the area, perimeter and altitude of the isosceles triangle. (b/4) * √(4a² – b²) is the formula that calculates the area of the isosceles triangle. P=2a+b is the formula that calculates the perimeter of the isosceles triangle. (b/2a) * √(4a² – b²) is the formula that calculates the altitude of isosceles triangles. 

The application of the isosceles triangle is present in numerous places in the real world. Some areas where the isosceles triangles are present are Catalan solids, pyramids, ancient architecture, designs, and monuments. 

The obtuse angle triangle contains two acute angles and one obtuse angle. We know that the sum of all the angles in a triangle is 180 degrees. And, according to the features of the obtuse angle, the angle is bigger than 90 degrees. Therefore, there can be only one obtuse angle. Subsequently, this is also why obtuse angle triangles have two acute angles. These features distinguish the obtuse angle triangle from the other angles.

The area and the perimeter of the obtuse angle triangle can be calculated with various formulas. Area= 1/2 * b* h, where the letter b signifies the triangle's base and the letter h denotes the triangle's height is the formula that calculates the area. Perimeter= a+b+bc, obtuse angle triangle where the letters a, b and c indicate all the sides of the triangle, is the formula that calculates the perimeter of the obtuse angle triangle. The perimeter of the obtuse angle triangle is the sum of all the triangle sides.

Some examples of real-life applications of obtuse angle triangles are the clock hands at four or the angle the laptop forms with its base when it opens are examples of obtuse angles.

A scalene triangle is a triangle where none of the sides is similar. All the sides of the triangle are different and have different angles. The angle opposite to the longest side of the triangle is the largest angle of the triangle, and the angle opposite the smallest side of the triangle is the shortest side of the triangle. Thus, the most crucial feature of these triangles is that they are always asymmetrical and are not congruent.

Simple formulas can calculate the area and the perimeter of the scalene triangles. Area= hbb/2 where hb indicates the triangle's height and the b denotes the triangle's base is the formula that calculates the area of the scalene triangle. Perimeter= a+b+c where the letters a, b and c indicate the triangle's sides. Therefore, the perimeter of the scalene triangle is the sum of all the triangle sides. Trusses used in roofs, and sails ramps are real-life examples of scalene triangles.

The equilateral triangle is a triangle that has all equal sides and all congruent angles. It is similar to the isosceles triangle, except that equilateral triangles have equal angles and sides. Since the sum of triangles is supposed to be 180 degrees in total according to the properties of a triangle, equilateral triangles have three angles of 60 degrees each, making the sum of the triangle 180 degrees. The shape of the equilateral triangle is also regular, unlike isosceles or scalene triangles.

Simple formulas can calculate the area and the perimeter of the equilateral triangle. Area= √3/4 a2, where the letter a represents the sides of the triangle, calculates the area of the equilateral triangle. Perimeter= 3*a, where the letter a means the sides of the triangle, calculates the perimeter of the equilateral triangle. The perimeter of the equilateral triangle is the addition of the sides of the equilateral triangle. Traffic signals where the traffic lights are in the shape of equilateral triangles are where you might see them every day.

An acute angle triangle is one where all the angles are less than 90 degrees. In other words, all the angles in the triangle are 60 degrees or less. 

Simple formulas can determine the area and the perimeter of the equilateral triangle. Area= (1/2)*b*h where the letter b denotes the triangle's base, and the letter h represents the height of the acute angle is the formula that calculates the area of the acute angle triangle. Perimeter= a+b+c where the letters a, b and c denote the sides of the triangle is the formula that calculates the perimeter of the acute angle triangle.

The right-angle triangle has only one right angle in the triangle. Mathematicians use this triangle more than the others due to its use in the Pythagoras theorem. According to the right angle triangle in the Pythagoras theorem, the hypotenuse is the root of the sum of the squares of the perpendicular and base sides.

Simple formulas can determine the area and the perimeter of the right-angle triangle. Area= ab/2 where the letters ab denote the sides of the triangle is the formula that calculates the area of the right-angled triangle. Perimeter= a+b√a2+b2 where the letters a and b indicate the triangle’s sides is the formula that calculates the perimeter of the right-angle triangle.

1. What are triangles? Name the different types of triangles.

Triangles are objects that have three sides and three angles. There are six types of triangles in total that exhibit different properties from each other. The types of triangles include: obtuse angle triangle, right-angle triangle, scalene triangle, equilateral triangle, isosceles triangle and acute angle triangle. These triangles have different properties, congruences, angles and lines.

2. List the different properties of triangles.

Triangles are geometric shapes that exhibit different properties. Listed below are some of the properties of triangles: 

1. The total sum of all the angles in a triangle must be 180 degrees. This triangle feature is also known as the angle sum property of a triangle. 

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

3. The sum of the length of two sides of a particular triangle is always greater than the third. 

4. The largest angle of the triangle is always on the opposite side of the triangle's longest side.

3. What are the features of isosceles triangles?

Isosceles triangles have two equal sides and angles and have one unequal side. Therefore, there are two similar base angles and one other angle in an isosceles triangle.

4. Differentiate between equilateral and scalene triangles.

Equilateral triangles have all equal sides. All the sides and the angles of the triangle are identical, and the angles of the equilateral triangle are 60 degrees each. On the other hand, scalene triangles are triangles with all uneven sides and angles. None of the angles or the lengths of the sides is similar to each other in scalene triangles. This is the basic difference between equilateral and scalene triangles.

There are different types of triangles that have disparate properties. Students have to study triangles with utmost concentration as it is a critical topic from the exam point of view. The NCERT Solutions related to this chapter also provides proper insight into the questions that might come related to this chapter. Students must regularly solve the NCERT Solutions of the Triangles chapter because it gives them a proper idea about their strengths and weaknesses. Solving NCERT solutions gives them a chance to improve their strengths and work on their weaknesses.