Learn Basic Geometrical ideas with Free Lessons & Tips

In the given figure where ll, mm, and nn are three parallel lines, and xx and yy intersect these lines, the points lying on the line xx would depend on the specific intersection points between xx and the lines ll, mm, and nn.

If we denote the intersection points between xx and ll, mm, and nn as AA, BB, and CC respectively, then the points lying on the line xx would include AA, BB, and CC.

So, the points lying on the line xx are AA, BB, and CC.

In this equilateral triangle ABC, AD is the median drawn from vertex A to the midpoint of BC (denoted as D), and AM is the altitude drawn from vertex A perpendicular to BC (denoted as M).

In an equilateral triangle, all medians are also altitudes. So, AD and AM coincide in this case.

A triangle has three vertices. Each vertex is a point where two sides of the triangle meet. So, regardless of the type of triangle (equilateral, isosceles, or scalene), it always has three vertices.

Through any two distinct points, exactly one line can be drawn. This is a fundamental postulate in geometry, known as the "line through two points" postulate. So, if you have two points, there is a unique line that passes through both of them.

The least number of line segments required to make a polygon is 3.

A polygon is a closed shape formed by straight lines. The simplest polygon is a triangle, which has three sides (and therefore three line segments).

So, with three line segments, you can form the smallest polygon, which is a triangle.

In the sketch, M1M1, M2M2, and M3M3 represent the medians of the triangle △ABC△ABC.

To name the medians:

• M1M1 is the median from vertex A to the midpoint of side BC.
• M2M2 is the median from vertex B to the midpoint of side AC.
• M3M3 is the median from vertex C to the midpoint of side AB.

Through one given point, infinitely many lines can be drawn. This is because any straight line can pass through a single point. So, for any point, there are infinite lines that can be drawn through it.