GeoGebra/Construction of right angled triangle

Triangle $$\langle A,B,C\rangle$$ is a three sided closed polygon. The sum of all the interior angles of triangle is 180˚.

Learning Task

 * Create a mathematical proof for that theorem, that the sum of all the interior angles of triangle is 180. Select two points $$A,B$$ of the triangle and create a parallel line $$g$$, which is to the line $$\overline{AB}$$ through the point $$C\in g$$ (i.e. $$\overline{AB} \, \| \, g$$ and $$C\in g$$).
 * the interior angles are denoted with $$\alpha, \, \beta , \, \gamma $$. Identify angles with the same values of $$\alpha $$ and $$ \beta $$.
 * Construct the triangle in Geogebra with the properties above and drag the points of the triangle. What are possible benefits and drawbacks for using Geogebra to get geometrical insights in the theorem above?

Use Cases for Geogebra - Algebra and Geometry
Geogebra is a mathematical application, as the name suggests it comprises the functions of both geometry and algebra. The application makes learning mathematics fun and the geometric construction part is more interactive and easy to work. We can construct triangle if any one of the following are given Three sides,Two sides and an angle between them,Two angles and the side between them,In the right angled triangle if the hypotenuse and leg We can construct a triangle using congruence of triangle criterion

Activities with Geogebra
CONSTRUCTION OF A RIGHT-ANGLED TRIANGLE WHEN THE LENGTH OF ONE LEG AND ITS HYPOTENUSE ARE GIVEN (RHS CRITERION)

To construct a triangle when the length of a side, hypotenuse, the angle at which right angle is formed are given, four steps are involved


 * Step 1: Draw a rough sketch of the triangle with given measure.
 * Step 2: First to draw the side whose length is given use the tool "line" in the tool bar and select the option "segment with given length". A dialogue box appears in which we have to enter the value of the given side and click OK. The line segment will be drawn.
 * Step 3: To construct the right angle at the given angle, the "perpendicular line" tool is selected in the tool bar and "perpendicular line" option is selected. To draw the perpendicular line the point of vertex at which the perpendicular line us to be drawn is selected and the line to which the line is to be drawn is clicked.
 * Step 4: To draw the hypotenuse a circle is drawn by using the tool "circle with center through a point" and selecting the option "circle with center and radius". The circle is drawn by selecting the given option and clicking on the point from which circle is to be drawn and giving the the measure of hypotenuse as the radius of the circle.
 * Step 5: The point of intersection of the circular arc on the perpendicular is marked using the tool “point” and selecting the option “intersect”.
 * Step 6: The right angled triangle is constructed finally by selecting the tool “polygon” and using the option “polygon”. The triangle is constructed by selecting all vertices in consecutive order and clicking on the first vertex again. Thus the triangle is constructed.