Triangle Centers and Properties

The video tutorial explains how to prove that the centroid and circumcenter of an equilateral triangle coincide. It begins by introducing the problem and then describes the process of finding the centroid by drawing medians. The tutorial uses congruence to demonstrate that the medians are equal and explains the properties of medians in an equilateral triangle. Finally, it concludes that the centroid and circumcenter are the same point, thus proving the initial statement.

What is the main objective of the problem discussed in the video?

• To prove that the centroid and circumcenter of an equilateral triangle coincide.

• To calculate the perimeter of an equilateral triangle.

• To prove that the centroid and circumcenter of an equilateral triangle are different.

• To find the area of an equilateral triangle.

What is a key property of an equilateral triangle?

• It has no medians.

• All angles are 90 degrees.

• All sides are equal.

• All sides are different.

How many medians does an equilateral triangle have?

• Three

• Two

• Four

• One

What is the circumcenter of a triangle?

• The point where all altitudes intersect.

• The midpoint of one side of the triangle.

• The center of the circle in which the triangle is inscribed.

• The point where all medians intersect.

Which theorem is used to prove the congruence of two triangles in the video?

• ASA Theorem

• SAS Theorem

• Pythagorean Theorem

• SSS Theorem

What is the result of proving triangle congruence using the SAS theorem?

• The triangles are isosceles.

• The triangles are congruent.

• The triangles are similar.

• The triangles are scalene.

How does the SAS theorem help in proving triangle congruence?

• By comparing two angles and a side.

• By comparing three sides.

• By comparing two sides and the included angle.

• By comparing three angles.

What is the common side in the triangles used for congruence proof?

• AB

• BC

• EC

• CD

What is the angle measure in an equilateral triangle?

• 60 degrees

• 120 degrees

• 45 degrees

• 90 degrees

What is the relationship between the medians in an equilateral triangle?

• They are all different in length.

• They do not intersect.

• They are all equal in length.

• They are parallel.