Triangle Properties and Angle Relationships

The video tutorial covers the basic properties of triangles, including their sides, angles, and area formula. It then addresses an ACT question involving an inscribed equilateral triangle and explains how to solve it. The tutorial also discusses special right triangles, such as 45-45-90 and 30-60-90 triangles, and their properties. Finally, it provides an overview of different triangle types, including obtuse and acute triangles, emphasizing the importance of understanding more than just basic properties for solving geometry problems.

How many sides does a triangle have?

• Three

• Five

• Four

• Two

What is the sum of the angles in any triangle?

• 360 degrees

• 270 degrees

• 180 degrees

• 90 degrees

What is the formula for the area of a triangle?

• Base times height

• Base plus height divided by 2

• Base times height divided by 2

• Base plus height

In the ACT question example, what type of triangle is ABC?

• Right

• Isosceles

• Equilateral

• Scalene

What is a key property of an equilateral triangle?

• All sides and angles are equal

• All angles are 90 degrees

• All sides are different

• One angle is greater than 90 degrees

What is the sum of the angles in an equilateral triangle?

• 90 degrees

• 270 degrees

• 360 degrees

• 180 degrees

Which triangle has all sides and angles equal?

• Scalene

• Equilateral

• Isosceles

• Right

What are the angles in a 45-45-90 triangle?

• 45, 45, 90

• 90, 90, 90

• 30, 60, 90

• 60, 60, 60

In a 30-60-90 triangle, what is the relationship between the hypotenuse and the shorter side?

• Hypotenuse is half the shorter side

• Hypotenuse is three times the shorter side

• Hypotenuse is twice the shorter side

• Hypotenuse is equal to the shorter side

In a 45-45-90 triangle, what is the relationship between the hypotenuse and the legs?

• Hypotenuse is half the legs

• Hypotenuse is equal to the legs

• Hypotenuse is twice the legs

• Hypotenuse is s√2 times the legs