Types of triangles. Properties of the angles and sides of a triangle

Types of triangles

1.An acute triangle is a triangle in which all of its angles are acute.
2. A rectangular triangle is a triangle in which one of its angles is a right angle. The sides of a rectangular triangle that form a right angle are called legs, and the side of the triangle that lies opposite the right angle is called the hypotenuse.
3. An obtuse triangle is a triangle in which one of the angles is obtuse.
4. An isosceles triangle is a triangle with two sides of equal length. The two equal sides of an isosceles triangle are called the lateral sides, and the third is called the base.
5. An equilateral or regular triangle is a triangle in which all three sides are of equal length.

Properties of triangle angles

6. The sum of the interior angles of a triangle is 180^∘.
7. The external angle of a triangle is equal to the sum of two internal angles that are not adjacent to it.
8. All angles of an equilateral triangle are equal to 60^∘.
9. In an isosceles rectangular triangle the acute angles are equal to 45^∘.

Relationships between angles and sides of a triangle

10. Opposite the larger angle in a triangle lies the larger side. Opposite the larger side of a triangle lies the larger angle.
11. Opposite equal sides of a triangle lie equal angles. Opposite equal angles in a triangle lie equal sides.

Triangle inequalities

12. In any triangle, the length of each side is less than the sum of the lengths of the other two sides.
13. In any triangle, the length of each side is greater than the absolute value of the difference between the lengths of the other two sides.