Where can the medians of a triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
A. I only
B. III only
C. I or III only
D. I, II, or II
since the medians are all inside the triangle, surely (A)
Try drawing some. A triangle can only have three acute angles, or one obtuse angles.
google triangle medians and see lots of images. You will see that no matter what the shape of the triangle, the medians must always intersect inside it.
In fact, if you look carefully, you will find a theorem that proves that they always intersect 2/3 of the way from each vertex to the opposite side.
Steve is so right thxxx
To determine where the medians of a triangle can intersect, let's start by understanding what medians are. The median of a triangle is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.
Now, let's consider the possible scenarios for the intersection of medians:
I. Inside the Triangle: In a typical triangle, the medians will intersect inside the triangle at a point called the centroid. The centroid is the point of concurrency of the medians, meaning all three medians intersect at a single point inside the triangle.
II. On the Triangle: In some special cases, such as an equilateral triangle or an isosceles triangle with two equal sides, the medians can intersect on the triangle itself. Specifically, the centroid coincides with one of the triangle's vertices, resulting in the medians intersecting on that vertex.
III. Outside the Triangle: Although unlikely, it is theoretically possible for the medians to extend beyond the triangle and intersect outside. However, this rarely occurs in practical applications and is not a common scenario.
Based on the above explanations, the correct answer is:
C. I or III only