Right Angle Triangle

Introduction

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

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 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 will 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. 

 

Ques. 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.

 

Conclusion

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 90degress is never formed in a right angle triangle. While constructing a right angle triangle, make sure to use the ruler and compass proper for adequate measurements.

FAQ (Frequently Asked Questions)

Ques1. Can you Explain in Detail about Acute, Right and Obtuse Angle Triangles for Better Clarification Between the Three?

Ans. The major difference between acute, right, and obtuse angle triangle is the angle made by the two adjacent sides of the triangle. 

  1. Acute angle triangle – when the angle formed between the two adjacent sides of the triangle is less than 90degree, it is known as acute angle triangle

  2. Right angle triangle – when the angle formed between the two adjacent sides of the triangle is equal to 90degree, it is known as the right-angle triangle. 

  3. Obtuse angle triangle – when the angle formed between the two adjacent sides of the triangle is of more than 90degree, then it is known as the obtuse angle triangle. 

Ques2. What is a Polygon and a Regular Polygon? In Which Category can we Classify a Triangle?

Ans. A polygon is a two-dimensional or a plane shape that has straight sides. A polygon should at least have 3 sides and angles, not necessarily equal to each other. 


On the other hand, a Regular polygon has all equal sides as well as all equal angles. The triangle is considered as a polygon because it has three sides and angles. It is not always necessarily a regular polygon. Only equilateral triangles can be considered as regular polygons as they have equal sides and equal angles.

Ques3. What is a Hypotenuse? Does only the Right-Angle Triangle have Hypotenuse?

Ans. The largest side in a right-angle triangle is called the hypotenuse. Since it is always opposite to the right angle, you must know that only right-angle triangles must have a hypotenuse and not the other types of triangles.