Equilateral Triangle Concepts and Theorems

This video tutorial covers the equilateral triangles theorem, starting with the definition of equilateral triangles as having three congruent sides. It explains that all equilateral triangles are also equiangular, meaning their angles are congruent. The video provides a proof of this theorem, using the properties of congruent sides and angles. It also discusses the isosceles triangle theorem, which states that if two sides of a triangle are congruent, the opposite angles are congruent. The tutorial concludes by summarizing the key points and emphasizing the relationship between equilateral and isosceles triangles.

What is a defining characteristic of an equilateral triangle?

• All sides are of different lengths.

• It has one right angle.

• It has two congruent sides.

• It has three congruent sides.

How is an equilateral triangle related to an isosceles triangle?

• Every equilateral triangle is also an isosceles triangle.

• Every isosceles triangle is also an equilateral triangle.

• They have no relation.

• They are the same.

According to the equilateral triangles theorem, what can be said about the angles of an equilateral triangle?

• They are all obtuse.

• They are all different.

• They are all congruent.

• They are all right angles.

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

• Draw a perpendicular bisector.

• State that the sides are congruent.

• Assume the angles are congruent.

• Calculate the area of the triangle.

Which theorem is used to prove that the angles in an equilateral triangle are congruent?

• Pythagorean theorem

• Triangle inequality theorem

• Isosceles triangle theorem

• Angle bisector theorem

If side AB is congruent to side AC in a triangle, which angles are congruent according to the isosceles triangle theorem?

• Angle A and angle C

• Angle A and angle D

• Angle B and angle C

• Angle A and angle B

What is the relationship between side congruence and angle congruence in an equilateral triangle?

• Angle congruence implies side congruence.

• Side congruence implies angle congruence.

• There is no relationship.

• Only one side needs to be congruent.

What is the final conclusion of the equilateral triangles theorem proof?

• Triangle ABC is scalene.

• Triangle ABC is equiangular.

• Triangle ABC is right-angled.

• Triangle ABC is obtuse.

What does the term 'equiangular' mean in the context of triangles?

• All angles are obtuse.

• All angles are right angles.

• All angles are equal.

• All angles are different.

Which of the following is NOT true about equilateral triangles?

• They are a type of isosceles triangle.

• They have one right angle.

• They have three congruent angles.

• They have three congruent sides.