Types of Triangles: Identifying and defining elements

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

Is the triangle in the drawing a right triangle?

It can be seen that all angles in the given triangle are less than 90 degrees.

In a right-angled triangle, there needs to be one angle that equals 90 degrees

Since this condition is not met, the triangle is not a right-angled triangle.

No

Given the values of the sides of a triangle, is it a triangle with different sides?

As is known, a scalene triangle is a triangle in which each side has a different length.

According to the given information, this is indeed a triangle where each side has a different length.

Yes

In a right triangle, the sum of the two non-right angles is...?

In a right-angled triangle, there is one angle that equals 90 degrees, and the other two angles sum up to 180 degrees (sum of angles in a triangle)

Therefore, the sum of the two non-right angles is 90 degrees

$90+90=180$

90 degrees

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 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

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 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

What kind of triangle is given here?

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

Scalene triangle

Choose the appropriate triangle according to the following:

Angle B equals 90 degrees.

Let's note in which of the triangles angle B forms a right angle, meaning an angle of 90 degrees.

In answers C+D, we can see that angle B is smaller than 90 degrees.

In answer A, it is equal to 90 degrees.

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

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

Below is the Isosceles triangle ABC (AC = AB):

In its interior, a line ED is drawn parallel to CB.

Is the triangle AED also an isosceles triangle?

To demonstrate that triangle AED is isosceles, we must prove that its hypotenuses are equal or that the opposite angles to them are equal.

Given that angles ABC and ACB are equal (since they are equal opposite bisectors),

And since ED is parallel to BC, the angles ABC and ACB alternate and are equal to angles ADE and AED (alternate and equal angles between parallel lines)

Opposite angles ADE and AED are respectively sides AD and AE, and therefore are also equal (opposite equal angles, the legs of triangle AED are also equal)

Therefore, triangle ADE is isosceles.

AED isosceles

ABCD is a square with AC as its diagonal.

What kind of triangles are ABC and ACD?

(There may be more than one correct answer!)

Since ABCD is a square, all its angles measure 90 degrees.

Therefore, angles D and B are equal to 90°, that is, they are right angles,

Therefore, the two triangles ABC and ADC are right triangles.

In a square all sides are equal, therefore:

$AB=BC=CD=DA$

But the diagonal AC is not equal to them.

Therefore, the two previous triangles are isosceles:

$AD=DC$

$AB=BC$

Right triangles

Is the triangle in the drawing an acute-angled triangle?

Yes

Is the triangle in the drawing an acute-angled triangle?

Yes

Is the triangle in the drawing an acute-angled triangle?

Yes

Given the values of the sides of a triangle, is it a triangle with different sides?

Yes

Given the values of the sides of a triangle, is it a triangle with different sides?

Yes