Medians divide into smaller triangles of equal area | Geometry | Khan Academy

TL;DR

Triangle medians bisect opposite sides and intersect at the centroid, dividing the triangle into six smaller triangles of equal area.

Transcript

But what I think about now is the if we're given some triangle, and here we have triangle ABC What are the medians of the triangle and how do they relate to each other and do they have some interesting properties, and you might guess that they do So the median is, if we start at one of the vertices so let's start at this one right over here And the... Read More

Key Insights

• 🙃 Triangle medians bisect opposite sides of the triangle.
• 🔺 Medians in a triangle intersect at a single point called the centroid.
• 🔺 The centroid is the center of gravity of a triangle.
• 🔺 Dividing a triangle into six smaller triangles using its medians results in equal areas.
• 🟰 Medians have equal length from the vertex to the centroid.
• 🫥 Medians are concurrent lines in a triangle.
• 🔺 The centroid is the balance point of a triangle.

Questions & Answers

Q: What is a median in a triangle?

In a triangle, a median is a line segment that starts at a vertex and bisects the opposite side. It divides the triangle into two equal parts.

Q: What is the centroid of a triangle?

The centroid of a triangle is the point where all three medians intersect. It is also the center of gravity of the triangle.

Q: Do all medians in a triangle intersect at a single point?

Yes, all medians in a triangle intersect at a single point called the centroid. This is a unique property of triangles.

Q: What is the significance of dividing a triangle into six smaller triangles using its medians?

Dividing a triangle into six smaller triangles using its medians results in each smaller triangle having equal area. This property is useful in various geometry problems and calculations.

Summary & Key Takeaways

• Triangle medians start at a vertex and bisect the opposite side, resulting in three medians that intersect at the centroid.

• The medians of a triangle have interesting properties, such as having equal lengths and intersecting at a single point.

• Dividing a triangle into six smaller triangles using its medians results in each smaller triangle having equal area.