Right Triangle

🏆Practice types of triangles

Definition of a right triangle

A right triangle is a triangle that has one right angle, meaning an angle of 90 degrees. Based on the fact that the sum of angles in any triangle is 180 degrees, we can conclude that the sum of the two remaining angles in a right triangle is 90 degrees. This means that both angles must be acute (less than 90 degrees).

Right Triangle

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Test yourself on types of triangles!

einstein

What kid of triangle is given in the drawing?

90°90°90°AAABBBCCC

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Here are some examples of right triangles:

Examples of right triangles

Exercise

For example, let's take any right triangle. It is known that one of the angles in this triangle is 45 degrees. We are asked to find the second acute angle in the given triangle.

Since this is a right triangle, meaning one of the angles equals 90 degrees, we can calculate and find that the second acute angle will be equal to 45 degrees. Why? Because it complements the first given acute angle to 90 degrees.

Diagram of a right triangle labeled with angles: B = 90°, C = 45°, and A = ?. The triangle illustrates a problem-solving exercise to determine the missing angle A using the triangle sum theorem. Featured in a tutorial on understanding angles in a right triangle.

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Examples with solutions for Types of Triangles

Exercise #1

What kid of triangle is given in the drawing?

90°90°90°AAABBBCCC

Video Solution

Step-by-Step Solution

The measure of angle C is 90°, therefore it is a right angle.

If one of the angles of the triangle is right, it is a right triangle.

Answer

Right triangle

Exercise #2

What kind of triangle is given in the drawing?

404040707070707070AAABBBCCC

Video Solution

Step-by-Step Solution

As all the angles of a triangle are less than 90° and the sum of the angles of a triangle equals 180°:

70+70+40=180 70+70+40=180

The triangle is isosceles.

Answer

Isosceles triangle

Exercise #3

What kid of triangle is the following

393939107107107343434AAABBBCCC

Video Solution

Step-by-Step Solution

Given that in an obtuse triangle it is enough for one of the angles to be greater than 90°, and in the given triangle we have an angle C greater than 90°,

C=107 C=107

Furthermore, the sum of the angles of the given triangle is 180 degrees so it is indeed a triangle:

107+34+39=180 107+34+39=180

The triangle is obtuse.

Answer

Obtuse Triangle

Exercise #4

What kind of triangle is given in the drawing?

999555999AAABBBCCC

Video Solution

Step-by-Step Solution

Given that sides AB and AC are both equal to 9, which means that the legs of the triangle are equal and the base BC is equal to 5,

Therefore, the triangle is isosceles.

Answer

Isosceles triangle

Exercise #5

Which kind of triangle is given in the drawing?

666666666AAABBBCCC

Video Solution

Step-by-Step Solution

As we know that sides AB, BC, and CA are all equal to 6,

All are equal to each other and, therefore, the triangle is equilateral.

Answer

Equilateral triangle

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