Understanding Triangles: Key Concepts and Theorems

This video reviews various properties of triangles, including perpendicular bisectors, angle bisectors, medians, and altitudes. It explains how these elements intersect at unique points like the circumcenter, incenter, centroid, and orthocenter, and discusses their significance in geometry.

What is the unique point called where the perpendicular bisectors of a triangle intersect?

• Centroid

• Orthocenter

• Incenter

• Circumcenter

Which of the following is true about the circumcenter of a triangle?

• It is the midpoint of the triangle's base.

• It is always inside the triangle.

• It is equidistant from the vertices of the triangle.

• It is equidistant from the sides of the triangle.

Where do the angle bisectors of a triangle meet?

• At the centroid

• At the circumcenter

• At the orthocenter

• At the incenter

What is the incenter of a triangle equidistant from?

• The height of the triangle

• The sides of the triangle

• The base of the triangle

• The vertices of the triangle

According to the angle bisector theorem, what is the relationship between the segments created by an angle bisector?

• They form a right angle.

• They are perpendicular to each other.

• They are proportional to the adjacent sides.

• They are equal in length.

What is the point called where the medians of a triangle intersect?

• Incenter

• Circumcenter

• Orthocenter

• Centroid

How does the centroid divide each median of a triangle?

• Into three equal parts

• In a 3:1 ratio

• In a 2:1 ratio

• Into two equal parts

What is a medial triangle?

• A triangle formed by the angle bisectors

• A triangle formed by the midpoints of the sides

• A triangle formed by the altitudes

• A triangle formed by the medians

Where do the altitudes of a triangle intersect?

• At the orthocenter

• At the centroid

• At the circumcenter

• At the incenter

Which statement is true about the orthocenter of a triangle?

• It is always inside the triangle.

• It is always outside the triangle.

• It can be inside or outside the triangle.

• It is the midpoint of the triangle's base.