Geogebra Tutorial 3 Constructing Asquare

GeoGebra Tutorial 3 – Constructing aSquare

Problem:How will you draw an equilateral triangle without using the Regular polygon tool?

In this tutorial, like Tutorial 2, we will mimic compass and straightedge construction using the circle tool, the parallel line tool, the perpendicular tool to construct a square instead of using the Regular polygon tool. We will also reinforce the use of the angle tool, this time, learn how to use it to measure angle using three points.

Figure 1 - Square formed from radii of a circle

The idea of our construction is to construct a circle with radius AB and construct lines parallel and perpendicular to it to form our square.

START / 1.) Open theGeoGebra window. We will not need theAlgebra windowand theCoordinate axesso we will hide them. To hide theCoordinate axes, click theViewmenu on the menu bar, and then clickAxes. To hide theAlgebra window, clickViewthen clickAlgebra window.
/ 2.) Click theSegment between twopointstool and click two distinct places on the drawing pad to construct segmentAB.
/ 3.) If the labels of the points are not displayed, click theMove button, right click each point and clickShow labelfrom the context menu. (Thecontext menu is the pop-up menu that appears when you right click an object.)
/ 4.) To construct a circle with centerApassing throughB, click theCircle with Center through Pointtool, click pointA, then click pointB. After step 4, your drawing should look like the one shown inFigure 2.
Figure 2 - Circle with center A and passing through B
/ 5.) To construct a line perpendicular toABand passing throughA,click the Perpendicular linetool, click segmentABthen click pointA.
/ 6.) To intersect the circle and the line, use theNew Pointtool and click one of the intersections. If the label of the third point is not shown, right click the point, then clickShow label. After step 6, your drawing should look like the one shown inFigure 3.

Figure 3 - Circle with radius AB and a line perpendicular to AB passing through A
/ 7.) Next, we construct a line parallel toABthen passing throughC. To do this, click the inverted triangle at the bottom right of thePerpendicular linetool, then choose theParallel linetool. Click segmentAB, then click pointC.
/ 8.) Now, we construct a line parallel toACand passing through pointB. To do this, with theParallel line toolstill active, click lineACthen click pointB.
/ 9.) Intersect the line passing through pointBand pointCto form pointD, the fourth vertex of the square. After step 9, your drawing should look like the one shown inFigure 3.

Figure 3 - Square formed from radii a circle
/ 10.) Using theMovebutton, move the pointAor pointB. What do you observe?
11.) Next we hide all the objects except the four points and segmentAB. To do this, right click each object and then uncheckShow Objectfrom the context menu.
/ 12.) To complete the square, connect pointsAandC, pointsCandD, and pointsBand with theSegment betweentwo points tool.
13. To verify that the quadrilateral that we created is indeed a square, right click each side and clickObject Properties.
14. In theObject Propertieswindow, select theBasictab. Be sure that the Show labelcheck box is checked and chooseValuefrom theShow labeldrop down list box. (see the last figure inTutorial 2)
/ 15. To measure angleA,click theAngle tool, and click the vertices in the following order: pointC, pointAand then pointB.

Figure 4 - Square ABCD with a reflex angle on vertex A
16. In case the angle formed is a reflex angle, right click the symbol (the green sector), clickObject Propertiesfrom the context menu.
17. In theBasic tabof theObject Propertieswindow, uncheck theAllow Reflex Anglecheck box, and then click theClosebutton.
18. Reveal the measure of the three other angles. Move pointAor pointB. What do you observe?
19.Explain why the construction above always results to a square.