assalamualaikum

Task 1

Build a triangle with three altitudes.

Draw three points, use line segment to complete the triangle.

When constructing the three altitudes, the point of intersection of the altitudes should always be displayed, as in task #5 (from the previous lesson), where the extensions of the altitudes to their intersection should be shown.

Draw three perpendicular lines using perpendicular line tool. Touch the line and than the point, it will aligned.

Use intersection tool . Give point D,E, and F

Remove the line using , show and hide tool .

Task2

Build a triangle. From vertex A, construct (show) the altitude, angle bisector, and median.
Show that the altitude is a perpendicular line.
Show that the median divides the opposite side in half.
Show that the angle bisector divides the angle into two equal parts.
Make sure the altitude, median, and angle bisector stand out to draw attention to them.
‼️You must construct and show one altitude, one median, and one angle bisector from the same vertex.

Angle Bisector

To construct base bisector, all we need to take perpendicular bisector, join the line with the each vertices. We can check the angles , which also shows here that angles are equal so it is angle bisector.

Altitude

To find altitude all we need a triangle. Use angle bisector tools for each vertices. Join the lines with vertices. Remove the extra lines. Join each intersection points.

Median

To find median we need three perpendicular bisectors lines. After that use intersection tool to assign Points as I shown in the figure. Hide the remaining part only the median triangle will left.

It is shown from figures that all the median divide the sides in half.

Task 3

The Basics of Medians
Build triangle ABC. Then, using the medians as the new triangle's vertices, construct a new triangle.
What properties does this triangle have?

To draw median , construct a triangle , use three perpendicular bisector tool.

Remove the line use hide and show tool

Join all the intersection point. It will make a second triangle, give name DEF TRIANGLE.

FIND distance from each vertices to mid point as we take D,,E and F as mid point. It show from the calculation that all this distance between vertic and their mid point is equal.

The value show the property of median .

Task 4

The Bases of the Altitudes
Build triangle ABC, then, using the bases of the altitudes as the vertices, construct another triangle.

Task 5

The Bases of the Angle Bisectors. Construct triangle ABC, then, using the bases of the angle bisectors as the vertices, construct another triangle. Show that the angles formed are exactly the angle bisectors.

Task 6

Display Four Triangles Together. Draw the four triangles: the main triangle ABC, and the triangles formed by the bases of the altitudes, angle bisectors, and medians. There should be four (or three) triangles on the drawing. (It is normal for the triangle formed by the bases of the altitudes to disappear.)

Draw a triangle A,B,C , first if all we draw altitude, than angle bisector and in last Median. As we can see all the triangle have one common point M. If we rotate each vertices. The the lines and points will move with it.