Learn Class 11 Math - Triangles

Triangles can be defined as a plane figure which has three straight sides and also three angles made by the intersection of these three sides.

Elements of a triangle include the vertices, sides and the angles of a triangle.

Angles of a Triangle

Angles of a triangle can be defined as the angles secured or marked by the intersection of two adjacent sides internally.

All the three angles of a triangle add up together to make 180° internally.

Types of Triangle

Equilateral triangle: they can be defined as triangles with all the three sides and the angles equal to each other. Each angle is 60° in case of equilateral triangles.
Right angle triangle: they can be defined as the triangles which have at least one angle equal to 90°
Scalene triangles: These triangles have all the three sides and the angles which are not equal to each other.
Isosceles triangle: A triangle of this type has at least two sides that are not equal to each other. Therefore, the angles adjacent to those two sides are also equal.

Perimeter:

Side 1 + side 2 + side 3 = perimeter.

Adding up all the three sides of a triangle will give the perimeter of a given triangle

Area:

½ × base × height = area.

This formula is useful for calculating the area of a given triangle.

Triangles Sample Questions for Class 11

Question 1

What type of triangle has sides 7, 10, 14?

A. acute

B. right

C. obtuse

Question 2

In a 30-60-90 triangle, the short leg measures 8 cm. What is the length of the hypotenuse?

A. 16sqrt3 \ "cm"

B. 24 \ "cm"

C. 8sqrt2 \ "cm"

D. 16 \ "cm"

Question 3

If one triangle can be mapped onto another triangle through a sequence of rigid transformations, which of the following MUST be true? Choose all that apply.

A. The name of the triangles is the same.

B. The corresponding sides of the triangles are congruent.

C. The corresponding angles of the triangles are congruent.

D. The orientation of the triangles is the same.

Question 4

Now that we have the lengths of the legs of the triangle, what theorem, property, or formula correctly relates them and why is it used?

A. The formula for the area of a triangle, A = 1/2 (y-3) * (x-4), since we know the height and base of the triangle.

B. Heron's Formula, A = sqrt(s*(s-a)*(s-b)*(s-c)), " where " s = (2 + (y-4)^2 + (x-3)^2 )/2, because the length of all three sides is known.

C. Pythagorean Theorem, (x-3)^2 + (y-4)^2 = 4, since the lengths of the three sides of the right triangle are known, and this introduces no extra variables.

D. Law of Cosines, |x-3|^2 = 4 + |y-4|^2 - 2*2*|y-4|*cos90°, because the lengths of the three sides of the triangle, and the measure of the right angle, are known, and this introduces no extra variables.

Question 5

Which of the following represents the length of the horizontal leg of the right triangle? (If need be, use the first correct answer in the first question if there were multiple correct answers.)

A. 3-x

B. x+3

C. |x-3|

D. (3-x)^2