Triangle Properties and Relationships

This video tutorial explains how to classify triangles based on their side lengths and angles. It covers the classification of acute, right, and obtuse triangles, and demonstrates how to use the Pythagorean theorem to determine the type of triangle. The video includes practice problems to illustrate the concepts and provides a method to find values that make a triangle acute.

What type of triangle has all angles less than 90 degrees?

• Obtuse triangle

• Equilateral triangle

• Right triangle

• Acute triangle

In a right triangle, what is the longest side called?

• Median

• Hypotenuse

• Height

• Base

According to the Pythagorean theorem, what is the relationship in a right triangle?

• a^2 + b^2 = 2c^2

• a^2 + b^2 < c^2

• a^2 + b^2 > c^2

• a^2 + b^2 = c^2

For an acute triangle, how does the sum of the squares of the two shorter sides compare to the square of the longest side?

• Twice as much

• Equal to

• Greater than

• Less than

In an obtuse triangle, how does the square of the longest side compare to the sum of the squares of the other two sides?

• Less than

• Greater than

• Half as much

• Equal to

Given a triangle with sides 3, 7, and 8, what type of triangle is it?

• Acute triangle

• Equilateral triangle

• Right triangle

• Obtuse triangle

If a triangle has sides 5 and 6, what is the maximum possible length for the third side to ensure the triangle is acute?

• 6.50

• 8.00

• 7.00

• 7.81

What is the approximate value of the square root of 61?

• 7.50

• 8.00

• 7.00

• 7.81

Which formula is used to determine if a triangle is acute?

• a^2 + b^2 = c^2

• a^2 + b^2 > c^2

• a^2 + b^2 < c^2

• a^2 + b^2 = 2c^2

What is the relationship between the sides of a triangle if it is obtuse?

• a^2 + b^2 > c^2

• a^2 + b^2 = c^2

• a^2 + b^2 < c^2

• a^2 + b^2 = 2c^2