Properties of Triangles and Theorems

This video tutorial covers the equilateral triangles theorem. It begins by defining an equilateral triangle as one with three congruent sides and explains that such triangles are also isosceles. The video then proves the equilateral triangles theorem, which states that equilateral triangles are equiangular. The proof involves showing that if all sides are congruent, then all angles are congruent, using the isosceles triangle theorem. The tutorial concludes with a summary of the proof and its implications.

What is the main goal of the lesson on the equilateral triangles theorem?

• To define a right triangle

• To define an equilateral triangle and prove the equilateral triangles theorem

• To prove the Pythagorean theorem

• To define a scalene triangle

What is an equilateral triangle?

• A triangle with one right angle

• A triangle with three congruent sides

• A triangle with two congruent sides

• A triangle with three different sides

How can you identify an equilateral triangle?

• By checking if it has two congruent sides

• By checking if it has three congruent sides

• By checking if it has one right angle

• By checking if it has no congruent sides

What does the equilateral triangles theorem state?

• All equilateral triangles have one obtuse angle

• All equilateral triangles are scalene

• All equilateral triangles are right triangles

• All equilateral triangles are equiangular

If a triangle has three congruent sides, what can be said about its angles according to the equilateral triangles theorem?

• The angles are all congruent

• The angles are all obtuse

• The angles are all different

• The angles are all right angles

What is the first step in proving the equilateral triangles theorem?

• Calculating the area of the triangle

• Drawing a right triangle

• Stating the given information

• Assuming the triangle is scalene

According to the proof, if side AB is congruent to side AC, which angles are congruent?

• Angle A and Angle B

• Angle A and Angle D

• Angle B and Angle C

• Angle A and Angle C

What theorem is used to prove that if two sides of a triangle are congruent, then the opposite angles are congruent?

• Pythagorean theorem

• Isosceles triangle theorem

• Scalene triangle theorem

• Right triangle theorem

If side AB is congruent to side BC, which angles are congruent?

• Angle A and Angle B

• Angle B and Angle C

• Angle A and Angle D

• Angle C and Angle A

What is the final conclusion of the proof?

• Triangle ABC is scalene

• Triangle ABC is obtuse

• Triangle ABC is right-angled

• Triangle ABC is equiangular