[Maths Class Notes] on Right Angle Triangle Pdf for Exam

A triangle is referred to as a regular polygon that has three sides. The unique property of a triangle is that the sum of any two sides of the triangle is always greater than the measure of the third side of the triangle. In simpler words, a triangle is just a closed figure of three sides that has a sum of its angles equal to 180degree. Each shape of the triangle is classified based on the angle made by the two adjacent sides of the particular triangle. 

  1. Acute angle triangle

  2. Right angle triangle 

  3. Obtuse angle triangle 


Right Angled Triangle

The right-angled triangle is the geometrical shape and it is considered as the basics of trigonometry. A right-angled triangle has 3 sides:

  1. Base

  2. Hypotenuse

  3. Height 

The angle formed between the base and the height of the triangle is always of 90degrees.


Properties of Right – Angled Triangle 

All the properties of the right-angled triangle are mentioned below:

  1. One angle of the triangle always measures 90degree.

  2. The hypotenuse is the longest side of the right-angle triangle. 

  3. The side that is opposite to the 90degree angle is the hypotenuse.

  4. The Sum of two interior angles of the right-angled triangle is always 90degree. 

  5. The sides adjacent to the 90degree/right angle in the triangle are known as the base and perpendicular of the triangle.

  6. When you draw the perpendicular from the right angle of the triangle and join it to the hypotenuse, you will always get three similar kinds of triangles. 

  7. Considering the fact, if one angle of the right-angle triangle is 90degree and the other two angles are of 45degree each, then this type of triangle is known as an Isosceles right-angled triangle. In this, the adjacent side to the angle of 90degree must be equal to each other. 

  8. If you draw a circle along the three vertices of the triangle, then the radius of the circle drawn will always be equal to half the actual length of the hypotenuse. 

  9. The two angles, other than the angle of 90degree in a right-angle triangle, are always acute angles. 

  10. The largest side of a right-angled triangle is known as the Hypotenuse.


Steps to Draw a Right-Angled Triangle

To draw a right-angle triangle is quite simple when the required information for the construction of the same is given or known to you. 

To construct a right-angle triangle, the measurement of the hypotenuse of the triangle and the measurement of either of the remaining two sides, base and perpendicular, must be given to you. So, let’s proceed in the form of activity. 

Question. The length of the hypotenuse of the triangle is 5cm and the length of the other side of the triangle is 3cm. Construct a right-angled triangle according to the given information. 

Aim – To Construct a Right-Angled Triangle

Material Required –  

  1. Ruler/scale

  2. Compass

  3. Pen or a pencil 

  4. Eraser 

  5. Sharper 

  6. Sheet 


Steps of Construction – 

  1. First, you have to draw a horizontal line on a sheet with the help of a ruler and a pencil. The line can be of any measurement. 

  2. Mark a point C on the horizontal line. 

  3. Now, set the width of the compass as 3cm using a scale. 

  4. Now, place the pointer of the compass on point C. 

  5. Mark one arc on both sides from point C. 

  6. Label the points where arcs cross the lines as P and A, respectively.

  7. Now, set the length of the hypotenuse in the compass, as given in the question. 

  8. Hence, the compass width is now set as 5cm. 

  9. Now place the pointer of the compass on point P. 

  10. Now draw an arc above point C by placing the compass on point P. 

  11. Now, repeat the previous step from point A. 

  12. Now, mark the point where two arcs from point A and Point P cross each other as B. 

  13.  Join points A and B using a scale 

  14. Join points B and C using a scale.

Right Triangle Formula

Pythagoras, the renowned Greek philosopher, derived an important formula for a right triangle. The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two legs, according to the formula. Pythagoras’ theorem was named after him. The following is a representation of the right triangle formula: The sum of the squares of the base and height equals the square of the hypotenuse.

We have the following in a right triangle: 

[(Hypotenuse)^{2} = (Base)^{2} + (Altitude)^{2}]

Pythagorean Triplet: The Pythagorean triplets are the three numbers that fulfill the preceding equation. For example, the Pythagorean triplet (3, 4, 5) is a Pythagorean triplet since [3^{2} = 9, 4^{2} = 16, and 5^{2} = 25] and 9 +16 = 25. As a result, [3^{2} + 4^{2} = 5^{2}]. The Pythagorean triplet is a set of three integers that meet this requirement. 

Perimeter of a Right Angle Triangle

The perimeter of a right triangle is equal to the sum of its three sides. It is the sum of the right triangle’s base, height, and hypotenuse. For example, the area of a right triangle ABC with sides AB, AC, and BC, the perimeter is equal to the sum of the sides
BC + AC + AB = (a + b + c) units. The perimeter has a length unit and is a linear value.

Area of a Right Angle triangle

The spread, or the amount of space filled by a right triangle, is determined by its area. It is equal to half of the product of the triangle’s base and height. Because it is a two-dimensional variable, it is expressed in square units. The base and altitude are the only two sides required to determine the right-angled triangle area.

The area of a right triangle may be calculated using the right triangle definition: A right triangle’s area is equal to (1/2 * base * height) square units.


Now you get a right-angle triangle ACB. The angle made at point C is of 90degree. The triangle constructed is as per the measurements given in the question. So, now we are clear about the fact that the longest side of a right-angle triangle is the hypotenuse of the triangle. The two angles, other than that of 90degree in a right angle triangle, are always acute angles, which means, they are always less than 90degree. Obtuse angles that are an angle of more than 90 degrees are never formed in a right-angle triangle. While constructing a right-angle triangle, make sure to use the ruler and compass properly for adequate measurements.

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