In this article, we will briefly learn everything necessary about triangles and also practice with some exercises!
Let's get started!
In this article, we will briefly learn everything necessary about triangles and also practice with some exercises!
Let's get started!
Calculate the area of the triangle ABC using the data in the figure.
The triangle is a figure composed of sides and the sum of all its angles always equals degrees.
There are several types of triangles:
Equilateral triangle - All sides (or edges) are equal, all angles are equal, and all heights are also the median and the bisector.
Isosceles triangle - It has two equal sides, two equal base angles, and the median is also the height and the bisector.
Right triangle - It has an angle of degrees formed by two legs. The side opposite the right angle is called the hypotenuse.
Scalene triangle - All sides of the triangle are different.
Click here for a more in-depth explanation about the types of triangles.
In any triangle, regardless of the type of triangle it is, the sum of all its angles equals .
In the equilateral triangle -> each angle is degrees.
In the isosceles triangle -> the two base angles are equal and the third completes the .
In the right triangle -> only one angle is and the other two complete the .
Another note:
In the special triangle of 90 º , 45 º , 45 º -> only one angle is and the other two are each, this creates a triangle that is both isosceles and right at the same time.
Exercise:
Given the following angles:
angle
angle
angle
Click here for a more in-depth explanation about the angles of triangles.
Calculate the area of the right triangle below:
Calculate the area of the following triangle:
Calculate the area of the following triangle:
Here we will present the general formula for calculating the area of triangles:
This formula is used to calculate the area of isosceles, equilateral, and scalene triangles.
Right triangle
length of the first leg length of the second leg
\frac{length~of~the~first~leg~\times ~length~of~the~second~leg
Click here for a more in-depth explanation about the area of the triangle.
The perimeter of the triangle is equal to the sum of the lengths of all sides.
In an equilateral triangle – all sides are equal, therefore, the perimeter of the triangle will be
In an isosceles triangle - there are two equal sides and it is convenient to remember this when we want to deduce the perimeter
Click here for a more in-depth explanation about the perimeter of the triangle.
Calculate the area of the following triangle:
Calculate the area of the following triangle:
Calculate the area of the triangle using the data in the figure below.
Triangles are considered congruent if all their angles and all their sides are equal respectively.
To prove that two triangles are congruent you must demonstrate one of the following congruence theorems:
ASA – angle, side, angle
If both triangles have 2 equal angles and the length of the side between them is also equal, the triangles are congruent.
SAS – side, angle, side
If both triangles have 2 equal sides and the adjacent angle is also equal, the triangles are congruent.
SSS - Side, side, side
If the lengths of all 3 sides are equal respectively in both triangles, the triangles are congruent.
SSA - Side, side, angle
If the 2 sides are equal in both triangles and so is the angle opposite the larger side, the triangles are congruent.
Click here for a more in-depth explanation on triangle congruence.
Similar triangles do not need to have identical areas as is the case with congruent triangles, it is enough that they have the same proportions.
To prove that two triangles are similar you must demonstrate one of the following similarity theorems:
AA – Angle, Angle
If two angles of one triangle are equal to two angles of the other, the triangles are similar.
SSS - Side, Side, Side
If in one triangle the three sides are proportional to the three sides of the other, the triangles are similar.
Click here for a more in-depth explanation on the similarity of triangles.
Angle A is equal to 30°
Angle B is equal to 60°
Angle C is equal to 90°
Can these angles form a triangle?
We add the three angles to see if they equal 180 degrees:
The sum of the angles equals 180, so they can form a triangle.
Yes
Given an equilateral triangle:
The perimeter of the triangle is 33 cm, what is the value of X?
We know that in an equilateral triangle all sides are equal,
Therefore, if we know that one side is equal to X, all sides are equal to X.
We know that the perimeter of the triangle is 33.
The perimeter of the triangle is equal to the sum of the sides together.
We replace the data:
We divide the two sections by 3:
11
Calculate the area of the triangle using the data in the figure below.
Calculate the area of the triangle using the data in the figure below.
Calculate the area of the triangle using the data in the figure below.