Triangle Properties and Theorems

This video is part two of an introduction to trigonometry, focusing on possible and impossible triangles. It explains the triangle inequality theorem, which states that the longest side of a triangle must be shorter than the sum of the other two sides, and the shortest side must be longer than the difference between the other two sides. The video provides practical examples, including 3-4-5, equilateral, and isosceles triangles, to illustrate these concepts. It concludes with advice for exam preparation and encourages viewers to engage with the content.

What is the main topic of this video?

• Geometry

• Algebra

• Calculus

• Trigonometry

According to the triangle inequality theorem, what must be true for the longest side of a triangle?

• It must be longer than the sum of the other two sides.

• It must be equal to the difference of the other two sides.

• It must be equal to the sum of the other two sides.

• It must be shorter than the sum of the other two sides.

What condition must the shortest side of a triangle satisfy?

• It must be longer than the difference between the other two sides.

• It must be equal to the sum of the other two sides.

• It must be equal to the longest side.

• It must be shorter than the difference between the other two sides.

How can the triangle inequality theorem be mathematically represented?

• a + b < c

• a - b > c

• |a - b| < c and a + b > c

• a + b = c

What is the purpose of evaluating given triangles in the video?

• To calculate their angles

• To check if they are possible triangles

• To determine their area

• To find their perimeter

What is a 3-4-5 triangle known as?

• Isosceles triangle

• Right triangle

• Equilateral triangle

• Scalene triangle

Which type of triangle has all sides equal?

• Isosceles triangle

• Scalene triangle

• Right triangle

• Equilateral triangle

What is the result when the longest side of a triangle is equal to the sum of the other two sides?

• An equilateral triangle

• An isosceles triangle

• A straight line

• A valid triangle

Why is a triangle with sides 10, 12, and 1 not valid?

• The longest side is shorter than the sum of the other two sides.

• The shortest side is longer than the difference between the other two sides.

• The longest side is longer than the sum of the other two sides.

• The shortest side is equal to the difference between the other two sides.

What is the conclusion of the video?

• A detailed explanation of calculus

• A discussion on geometry

• A farewell and best wishes for exams

• A summary of algebra concepts