Understanding Triangle Properties

The video tutorial demonstrates that if the orthocenter and centroid of a triangle coincide, the triangle must be equilateral. It reviews the definitions of orthocenter and centroid, sets up assumptions, and uses congruency arguments to prove the triangle's equilateral nature. The tutorial concludes by showing that all angles and sides are equal, confirming the triangle's equilateral property.

What is the orthocenter of a triangle?

• The point where the three medians intersect

• The point where the three altitudes intersect

• The point where the three perpendicular bisectors intersect

• The point where the three angle bisectors intersect

If the orthocenter and centroid of a triangle are the same, what can be inferred about the triangle?

• It is an equilateral triangle

• It is a right triangle

• It is an isosceles triangle

• It is a scalene triangle

What additional property does the triangle have when its orthocenter and centroid coincide?

• It is also the orthocenter

• It is also the incenter

• It is also the circumcenter

• It is also the excenter

Which triangles are compared using the side-angle-side (SAS) congruency in the proof?

• Triangles AFG and DFG

• Triangles AFG and CBG

• Triangles AFG and EFG

• Triangles AFG and BFG

What is the significance of vertical angles in the congruency argument?

• They help establish equal medians

• They help establish equal side lengths

• They help establish equal altitudes

• They help establish equal angles

How are the inner angles of the triangle shown to be equal?

• By using the properties of medians

• By using the properties of altitudes

• By using the properties of circumcenter

• By using congruent triangles and vertical angles

What is the measure of each angle in the equilateral triangle?

• 120 degrees

• 90 degrees

• 60 degrees

• 45 degrees

What conclusion is reached about the triangle when all angles are shown to be equal?

• It is a scalene triangle

• It is a right triangle

• It is an isosceles triangle

• It is an equilateral triangle

What is the relationship between the angles in the smaller triangles and the main triangle?

• The angles in the smaller triangles are equal to the main triangle

• The angles in the smaller triangles are unrelated to the main triangle

• The angles in the smaller triangles are half of the main triangle

• The angles in the smaller triangles are double the main triangle

What is the final step in proving the triangle is equilateral?

• Showing all medians are equal

• Showing all sides are equal

• Showing all angles are equal

• Showing all altitudes are equal