**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.

Can a right triangle be equilateral?

**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

Choose the appropriate triangle according to the following:

Angle B equals 90 degrees.

Question 2

Does every right triangle have an angle? The other two angles are?

Question 3

Does the drawing 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 $240°$.

Do you know what the answer is?

Question 1

Does the drawing show an obtuse triangle?

Question 2

Does the drawing show an obtuse triangle?

Question 3

Does the drawing show an obtuse triangle?

Related Subjects

- Area
- Area of Equilateral Triangle
- Area of a Scalene Triangle
- Area of Isosceles Triangle
- Area of a Deltoid (Kite)
- The Area of a Rhombus
- Congruent Triangles
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- Relations Between Sides of a Triangle
- Perimeter
- Perimeter
- Perimeter
- Perimeter
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