Medians in Triangle ABC

The video explains the concept of a median in a triangle, which is a line segment joining a vertex to the midpoint of the opposite side. It uses triangle ABC to illustrate this concept, showing that segments AX, BY, and CZ are medians because they connect vertices A, B, and C to the midpoints of the opposite sides, respectively. The video emphasizes that each triangle has three medians.

What is a median in a triangle?

• A segment that divides the triangle into two equal areas

• A line that bisects an angle

• A segment joining a vertex to the midpoint of the opposite side

• A line parallel to one side of the triangle

In triangle ABC, which segment is a median?

• Segment AC

• Segment AX

• Segment BC

• Segment AB

Why is segment AX considered a median in triangle ABC?

• Because A is a vertex and X is the midpoint of the opposite side

• Because AX bisects angle BAC

• Because AX is perpendicular to BC

• Because AX is the longest side

How many medians does triangle ABC have?

• Four

• Three

• Two

• One

Which segment is another median in triangle ABC?

• Segment BY

• Segment BX

• Segment CY

• Segment CZ

What makes segment BY a median in triangle ABC?

• B is a vertex and Y is the midpoint of the opposite side

• BY is the longest side

• BY is parallel to AC

• BY bisects angle ABC

Which segment is the third median in triangle ABC?

• Segment AB

• Segment AX

• Segment CZ

• Segment BY

Why is segment CZ considered a median in triangle ABC?

• CZ bisects angle ACB

• CZ is perpendicular to AB

• CZ is the longest side

• C is a vertex and Z is the midpoint of the opposite side