Types of Triangles in Euclidean Geometry

The video tutorial explains the basic properties and types of triangles, including classifications by angles (acute, obtuse, right) and by sides (scalene, isosceles, equilateral). It also covers special right triangles like 45-45-90 and 30-60-90 triangles. The tutorial further explores angle relationships within triangles and the fundamental reasoning in geometry, emphasizing how angles in a triangle always sum to 180 degrees and how this knowledge can be applied to solve geometric problems.

What is the maximum number of obtuse angles a triangle can have?

• Three

• One

• Two

• None

Which type of triangle has all sides of different lengths?

• Equilateral

• Isosceles

• Scalene

• Right

In a 30-60-90 triangle, what is the ratio of the lengths of the sides?

• 1:1:√2

• 1:√3:2

• 1:2:√3

• 1:1:2

If two angles in a triangle are known, how can you find the third angle?

• Add the two known angles

• Subtract the sum of the two known angles from 180

• Multiply the two known angles

• Divide the sum of the two known angles by 2

What is the relationship between an exterior angle and the two non-adjacent interior angles of a triangle?

• The exterior angle is equal to the sum of the two non-adjacent interior angles

• The exterior angle is equal to the difference of the two non-adjacent interior angles

• The exterior angle is twice the sum of the two non-adjacent interior angles

• The exterior angle is half the sum of the two non-adjacent interior angles