SLC S23 Week2 || Geometry with GeoGebra: The Triangle and Its Elements

Welcome, my lovely friends, to this entry for this week; it feels good to have you here!

To start with, I created three vertices, A, B, and C, as can be seen below.

Next, I joined these points using a segment after which I used the appropriate tool to insert the altitudes.

After inserting the altitudes, I tried moving the triangle from the three different points or vertices. The movement of the triangle is illustrated in the images below.

Constructing an altitude from vertex A, the first step was to create the three vertices of the triangle; ABC.

Afterward, I joined them using the segment tool to form a triangle ABC. Thereafter, I inserted a perpendicular line from vertex A to intersect line BC.

As shown below, the point of intersection is labeled D. The segment tool was used to join the vertex A to the point of intersection D which forms the altitude.

The perpendicular line was afterwards removed to have the altitude stand alone which is seen in a different color. To confirm the validity of the altitude, I tried moving the triangle from vertex A.

Also, the triangle was moved from vertex B and C, respectively, and the effects of the movement are illustrated below.

Constructing the angle bisector from vertex A. Since I already have my three vertices ABC, I went straight away to make an angle bisector from vertex A to bisect line AB.

The point of intersection is labeled D, and using the segment tool, a line is drawn from vertex A to D, and this forms our bisector. This is given a different color.

Afterwards, the angle bisector is removed, leaving the segment line from vertex A and to the point of intersection D, which forms the angle bisector. The triangle is then moved from vertex A and the movement is shown below.

Furthermore, the triangle is moved from vertex B and C and the effects can be seen below.

Constructing the median from the vertex A. In doing this, I quickly called back my three vertices ABC.

Then I inserted three perpendicular lines which intersect and divide each line of vertices into two equal halves. The intersection points were labeled D, E, and F as shown below.

Afterward, the perpendicular bisectors were removed, and the intersections were connected to the three vertices using a segment, and the intersection points were renamed to M1, M2, and M3 (indicating the three medians) while the centroid is denoted by o. The triangle is moved from vertex A and the effect can be seen below.

Also, the triangle is moved from vertices B and C and the image below shows the effects of the movement.

I built a triangle ABC

Then, I used three perpendicular lines to locate the median points, which are labeled D, E, and F.

After the above, the perpendicular lines were removed, leaving behind the median points, which were joined using a segment to form the triangle DEF.

I built triangle ABC and then inserted three perpendicular lines to intersect the three lines of triangle ABC from the three different vertices.

The points of intersections were labeled DEF respectively, after which the perpendicular lines were removed, leaving behind the intersection points, which are connected by a segment to form the triangle DEF, as seen below.

I constructed triangle ABC.

I inserted three angle bisectors to bisect the three lines of triangle ABC from the three different vertices. The intersection points were denoted by DEF.

In the next step, the angle bisectors were removed to have just intersection points which are the bases of the angle bisectors. They were joined using a segment to form the triangle DEF.

First, I constructed triangle ABC and then inserted three perpendicular lines to intersect the three lines of triangle ABC from the three different vertices, the bases of the altitudes.

The intersection points, which are the bases of the altitudes, are labeled DEF, after which the perpendicular lines were removed to have the three points of intersections.

These points of intersections are the bases of the altitudes connected by a segment forming the second triangle DEF. After that, three angle bisectors were also drawn and intersected the first triangle from the three vertices ABC.

The intersection points of the angle bisector, which are also its bases, are observed to be EGH, which were also joined using a segment to form the third triangle EGH.

In getting the next triangle using the bases of the median, three perpendicular lines are inserted, which intersect and divide each line of the first triangle ABC into two equal halves, giving rise to the bases of the medians. The medians are denoted by EIJ.

These bases of the medians EIJ are equally joined using a segment to form the fourth triangle EIJ as seen below.

From the above, we can observe that the three interior triangles have a common point of intersection which is E.

Thank you

Am inviting @xkool24, @lirvic, and @ngoenyi