Understanding Triangle Medians and Centroids

The video tutorial explains the properties of triangle ABC, where sides AB, BC, and AC are given. It introduces the concept of medians and centroids, showing that the intersection of medians is the centroid. The tutorial then explores the rotation of triangle ABC by 180 degrees about the centroid, forming a new triangle A'B'C'. It discusses the congruency of triangles formed and calculates the area of the union of triangles ABC and A'B'C'. The video concludes with a detailed calculation of the area of triangle ABC using trigonometry and the law of cosines.

What is the length of side AC in triangle ABC?

• 13

• 14

• 15

• 16

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

• Incenter

• Centroid

• Orthocenter

• Circumcenter

After rotating triangle ABC 180 degrees about the centroid, which line is parallel to line BC?

• B'C'

• A'C'

• A'B'

• C'A'

How many congruent triangles make up the star shape formed by the union of triangles ABC and A'B'C'?

• 6

• 12

• 9

• 15

What is the relationship between the distance from the centroid to a vertex and the distance from the centroid to the midpoint of the opposite side?

• Half as long

• Equal

• Twice as long

• Three times as long

Which theorem is used to calculate the height of triangle ABC?

• Pythagorean Theorem

• Heron's Formula

• Law of Cosines

• Law of Sines

What is the area of triangle ABC?

• 84

• 108

• 96

• 72

What is the ratio of the area of the star shape to the area of triangle ABC?

• 5/4

• 6/5

• 4/3

• 3/2

How many congruent triangles originally made up triangle ABC?

• 6

• 9

• 12

• 15

What is the final calculated area of the star shape?

• 112

• 104

• 120

• 96