Question

which diagram represents the theorem that the medians of a triangle intersect at a point?
option 1
option 2
option 3
option 4

Explanation:

Step1: Recall the median definition

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. So, in a diagram representing medians intersecting, we should see segments from each vertex to the midpoint of the opposite side (marked with midpoint indicators like equal segments) and all three medians intersecting at a single point (the centroid).

Step2: Analyze each option

• Option 1: Contains right angles, likely representing altitudes (perpendicular segments from vertex to opposite side), not medians.
• Option 2: Contains angle markings, likely representing angle bisectors (segments dividing angles), not medians.
• Option 3: Contains right angles and perpendicular symbols, likely representing perpendicular bisectors (or altitudes), not medians.
• Option 4: Has segments from each vertex to the midpoint of the opposite side (marked with equal segment symbols, indicating midpoints) and all three segments intersect at a point, which is the centroid (where medians intersect).

Answer:

Option 4