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

^{The Triangle and Its Elements}

Hello steemians!

Here I bring to you my entry on the Steemit learning challenge of S23W2. On the main topic geometry and algebra, studying triangle and its elements.

Task 1: Building a triangle with three altitudes.

In order to create a triangle with 3 Altitude, We start by going under the polygon section and then clicking on the first polygon which indicates a triangle.

From here we are able to create triangle ABC and then followed by the various attitudes. By definition, an attitude is a line From the vertex of a line segment to the opposite side of the triangle.

The 3 Basic altitude We are going to see in our diagram: Aa, Bb, and Cc. Among these altitudes We are going to see another Point, O known as the orthocenter Which is a general point in which all the altitudes intersect.

Construction:

Stop by drawing the triangle ABC using the polygon property which is on the first options in the extreme left of the polygon tools.
move under The construct section and choose perpendicular lines.
By clicking on the A and moving today opposite line
BC We construct altitude Aa
click on the second point B and move to the line AC To construct altitude Bb
click on the point C I'll move to the opposite line AB To construct altitude Cc.
proceed by constructing line segments on the three attitudes each.
hide the perpendicular lines and the line segments will remain on the various intersections.
move to the anger section and select angle size of 90°.
click from the orthocenter and move to each of the Three sides to construct right angles. Hide the angles within.
create an extension which is going to allow the right angles to move beyond the triangle dimensions at fixed points.

Task 2:Build a triangle

In this section, we are going to use the polygon to create our triangle ABC again. From which we will be able to attribute the following properties like altitude, midpoint s. And line segments.

under the polygon section, create a triangle with three points ABC.

Altitude :

Select perpendicular line, click on the Point A And move to the side BC to create the altitude A.
Select the angle tools And click on Angle size And set it to 90 to create an angle of 90°. This will ensure the people perpendicularity of the lines.
To make the altitude unique, we are going to attribute some colors to eat by right clicking and selecting an appropriate color.

The median line:

under the construction tools, select midpoint of the line BC and name it F.
click on the segment line, Select point A and move to the point M To create a medium AF.
To ensure that BC divides the median into two, we are going to select the distance tool to ensure that the distance BM equals the distance CF.

Angle Bisector for A:

Select point B, A, and C To create an angle bisector for triangle BAC.
click on the point AB followed by point A and the angle bisector and show that the angles are equal to AC.
We can make this unique by attributing some colors to make it stand out.

Task 3. The Basics of Medians

Construction of the triangle.

Under polygon tool, use the first option to construct the triangle ABC.

Midpoint section, find a million of AB, BC and CA using the midpoint or Center.

Label the midpoint M1 M2 M3, use the line segments to connect the points M1 M2 M3.

We proceed by right clicking on each segment, proceed to object properties, style and followed by decoration to show that the sides of the halves are equal.

Use distance tool tool to measure the length of triangle M1 M2 M3 and compare it to triangle ABC.

using angle tool, measure the angle of triangle M1 M2 M3 and compare it to triangle ABC.

Properties.

The area of triangle M1M2M3 is ¼ times the area of triangle ABC.
Triangle ABC is similar to triangle M1M2M3 and the ratio of their sides is in the ratio 1:2.
The angle B is equal to M3, the angle A is equal to angle M2 and and angle C equals angle M1.
AM1M2C together forms a parallelogram and so is the rest of the constitution point.

Task 4: The Bases of the Altitudes

To begin with, I start by creating the triangle, ABC using this polygon first option. From here, I construct you sure the attitudes with respect to the sides AB, BC, and AC. From here, I am going to replace The bisector line with a line segment. The point where the attitudes meet is the centroit And I will name it G.

After which I add another triangle which is going to fit at the vertex of the various attitudes. Moving on from here, I at the anger bisector To show that the attitudes make an anger of 90° with the sides. We can see the results in the image below.

Task 5:The Bases of the Angle Bisectors

So far, we are still going to use the polygon to create our triangle ABC. From which we are you going to use angle bisector for each of the points A,B, and C. From here, using the vertices of the angle bisectors. We proceed to create another triangle.

From here we are going to demonstrate that the angles are evenly bisected. First, we located the centroid of the bisectors. Then use the segment lines to create lines to the Center underlying properties we are going to use the dotted lines to replace the original line.

We proceed to measure the angles for each of the sides and show that they are all divided evenly. This is possible using the angle tools first option.

Task 6: Display Four Triangles Together

This task require us to apply a combination of all the Some of the other steps, in the same drawing. As usual, we begin by creating our triangle ABC. From here, we are going to create An attitude for each of the corresponding sites to A, B and C. We use the vertex of these attitudes to create a triangle.

Secondly, we create the median of AB, BC, and AC. We use the points of the medians to create another triangle.

Lastly, we create an Angle bisector. For each of the Angles, A, B & C. Using the vertices of the Angle bisector, We create the third triangle. We can combine this with question 5 to show also that the angles bisect equally And also to avoid repeating multiple steps.

The triangle form By the altitude is labeled A1A2A3
The triangle formed by the median is labeled M1M2M3
The triangle Formed by the bisector Is labeled B1 B2 B3.

From the above image, if we move One angle of the triangle ABC. And make it closer to 45°, we see that the triangle for altitude completely disappears as it was mentioned in the main lesson of this contest.

Animation

Finally, this brings us to the end This week's lesson. It was an interesting exercise and I am so happy to have learned a lot. With this exercises I will be able to apply graphs and shapes in Georgia bro in my teaching notes as well. It's a great thing which I didn't know about, but so far I believe I am going to make good use of this. Thanks to @sergeyk For the amazing lesson.

To conclude, I would like to invite the following persons to joinly participate with us in this contest.

@chant, @wirngo and @fombae.

Credit to: @rafk