Constructing Triangles with Constraints

The video tutorial explains the process of constructing triangles with specific side lengths. It demonstrates why a triangle with sides 2, 2, and 5 cannot be constructed due to the triangle inequality theorem. The concept of a degenerate triangle is introduced, where the sum of two sides equals the third side, resulting in no area. The tutorial then shows how a triangle with sides 3, 3, and 5 can be constructed, emphasizing that the longest side must be shorter than the sum of the other two sides for a valid triangle.

What is the sum of the lengths of the two shorter sides in the first triangle discussed?

• 4

• 3

• 5

• 6

Why can't a triangle with sides 2, 2, and 5 be constructed?

• It forms a square

• Sides are too short

• Violates triangle inequality

• Sides are too long

What type of triangle is formed when sides are 2, 2, and 4?

• Degenerate

• Isosceles

• Right

• Equilateral

What happens to the angles in a degenerate triangle formed by sides 2, 2, and 4?

• They total 180 degrees

• They become 0 degrees

• They are obtuse

• They are acute

What would happen if the points in a degenerate triangle with sides 2, 2, and 4 were moved outward?

• Nothing would change

• They would separate further

• They would overlap

• They would form a non-degenerate triangle

Which set of side lengths can form a non-degenerate triangle?

• 2, 2, 5

• 3, 3, 5

• 2, 2, 4

• 1, 1, 3

What is the necessary condition for side lengths to form a non-degenerate triangle?

• All angles are less than 90 degrees

• All sides are equal

• Any two sides sum more than the third

• Longest side equals sum of other two

In a triangle with sides 3, 3, and 5, what would happen if the two shorter sides were rotated inward?

• They would touch at one point

• They would separate

• They would overlap

• They would form a line

Can a triangle with sides 3, 3, and 5 be rotated to form a different triangle?

• Yes, into an equilateral

• No, it remains the same

• Yes, into a right triangle

• No, it becomes degenerate

What unique feature does the triangle with sides 3, 3, and 5 have?

• It has an area of zero

• It is the only possible configuration

• It has one obtuse angle

• It can change shapes