**An acute triangle has all acute angles**, meaning each of its three angles measures less than $90°$ degrees and the sum of all three together equals $180°$ degrees.

**An acute triangle has all acute angles**, meaning each of its three angles measures less than $90°$ degrees and the sum of all three together equals $180°$ degrees.

In a right triangle, the side opposite the right angle is called....?

**Next, we will look at some examples of acute triangles:**

**Assignment:**

Determine which of the following triangles is obtuse, which is acute, and which is a right triangle:

**Solution:**

**A.** We will examine if the Pythagorean theorem holds for this triangle:

$5²+8²=9²$

$25+64=81$

$89>81$

The sum of the squares of the perpendicular sides is greater than the square of the remaining side, therefore it is an acute-angled triangle.

**B.** Now we will examine this triangle:

$7²+7²=13²$

$49+49=169$

$169>98$

The sum of the squares of the perpendicular sides is greater than the square of the remaining side, therefore it is an obtuse-angled triangle.

$10.6≈\sqrt{113}$

**C.** The longest side of the 3 will be treated as the hypotenuse.

$7²+8²=\sqrt{113}²$

$49+64=113$

$113=113$

The Pythagorean theorem holds true and therefore triangle 3 is a right triangle.

**Answer:**

A-acute angle acute B-obtuse angle obtuse C-right angle right.

Test your knowledge

Question 1

In an isosceles triangle, what are each of the two equal sides called ?

Question 2

In a right triangle, the two sides that form a right angle are called...?

Question 3

Does the diagram show an obtuse triangle?

**Let's look at 3 angles**

Angle A is equal to $30°$

Angle B is equal to $60°$

Angle C is equal to $90°$

**Task:**

Can these angles form a triangle?

**Solution:**

$30+60+90=180$

The sum of the angles in a triangle is equal to $180°$,

therefore these angles can form a triangle.

**Answer:**

Yes, since the sum of the internal angles of a triangle is equal to $180°$.

Angle A is equal to $90°$

Angle B is equal to $115°$

Angle C is equal to $35°$

**Task:**

Can these angles form a triangle?

**Solution:**

$90°+115°+35°=240°$

The sum of the angles is greater than $180°$,

therefore these angles cannot form a triangle.

**Answer:**

No, since the sum of the internal angles must be $180°$, and in this case the angles add up to $240°$.

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 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

What kind of triangle is given here?

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

Scalene triangle

Do you know what the answer is?

Question 1

Does the diagram show an obtuse triangle?

Question 2

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

Question 3

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

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