Isosceles triangle - Examples, Exercises and Solutions

What kid of triangle is given in the drawing?

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.

Right triangle

What kind of triangle is given in the drawing?

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

$70+70+40=180$

The triangle is isosceles.

Isosceles triangle

What kid of triangle is the following

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°,

$C=107$

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

$107+34+39=180$

The triangle is obtuse.

Obtuse Triangle

What kind of triangle is given in the drawing?

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.

Isosceles triangle

Which kind of triangle is given in the drawing?

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.

Equilateral triangle

What kind of triangle is given here?

Since none of the sides have the same length, it is a scalene triangle.

Scalene triangle

Is the triangle in the drawing a right triangle?

Since we see the symbol that represents an angle equal to 90 degrees, indeed this is a right-angled triangle.

Yes

Calculate the size of angle X given that the triangle is equilateral.

Remember that the sum of angles in a triangle is equal to 180.

In an equilateral triangle, all sides and all angles are equal to each other.

Therefore, we will calculate as follows:

$x+x+x=180$

$3x=180$

We divide both sides by 3:

$x=60$

60

What kind of triangle is the following

Since in the given triangle all angles are equal, all sides are also equal.

It is known that in an equilateral triangle the measure of the angles will always be equal to 60° since the sum of the angles in a triangle is 180 degrees:

$60+60+60=180$

Therefore, it is an equilateral triangle.

Equilateral triangle

Given an equilateral triangle:

What is its perimeter?

Since the triangle is equilateral, that is, all sides are equal to each other.

The perimeter of the triangle is equal to the sum of all sides together, the perimeter of the triangle in the drawing is equal to:

$5+5+5=15$

15

Below is an equilateral triangle:

If the perimeter of the triangle is 33 cm, then 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, then 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:

$x+x+x=33$

$3x=33$

We divide the two sections by 3:

$\frac{3x}{3}=\frac{33}{3}$

$x=11$

11

Look at the isosceles triangle below:

What is its perimeter?

Since we are referring to an isosceles triangle, the two legs are equal to each other.

In the drawing, they give us the base which is equal to 4 and one side is equal to 6, therefore the other side is also equal to 6.

The perimeter of the triangle is equal to the sum of the sides and therefore:

$6+6+4=12+4=16$

16

What is the perimeter of the given isosceles triangle?

Due to the fact that the the triangle is isosceles, its two legs are equal to one another.

Therefore, the base is 7 and the other two sides are 12.

The perimeter of a triangle is equal to the sum of all the sides together:

$12+12+7=24+7=31$

31

The two legs of the triangle are equal. Calculate the perimeter of the triangle.

Since the two legs are equal, we can claim that:

$AB=AC=9$

The perimeter of the triangle is equal to the sum of all sides, meaning:

$AB+AC+BC$

Let's substitute the known data and calculate the perimeter:

$9+9+3=18+3=21$

21

Can a triangle have more than one obtuse angle?

If we try to draw two obtuse angles and connect them to form a triangle (i.e., only 3 sides), we will see that it is not possible.

Therefore, the answer is no.

No