how to draw an equilateral triangle

Tutorial: Constructing an Equilateral Triangle

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

Yous can follow this tutorial step by footstep by opening the GeoGebra window.

In this tutorial, we will mimic compass and straight edge structure using the circle tool. The idea is to use the intersections of two circles and the two centers to form as triangles as shown beneath.

Figure one - An equilateral triangle formed by radii of two circles

In amalgam our triangle, we are going to acquire how to employ the circle tool, and how to display interior angle measure out of a polygon and length of segments. Note that we can too depict a regular polygon of any side past using the Regular polygon tool.

i Nosotros will not need the Algebra window and the Coordinate axes so we will hide them. To hibernate the Coordinate axes, click the View menu on the menu bar, and so click Axes. To hide the Algebra window, click View so click Algebra window.

2 Click the Segment between 2 points tool, and click two singled-out places on the drawing pad to construct segment AB.

3 If the labels of the points are not displayed, click the Movement button, right click each point and click Show characterization from the context bill of fare. (The context menu is the popular-up menu that appears when you lot correct click an object.)

4 To construct a circle with center A passing through B, click the Circle with Eye through Point tool, click point A, and then click point B. After footstep 4, your drawing should look like the one shown in Figure ii.

Figure 2 - Circumvolve with center A and passing through B.

five To construct some other circle with center B passing through A, with the Circle with Center though Point still active, click point B so click indicate A.

6 Side by side, nosotros accept to intersect the circles. To intersect the 2 circles, click the inverted triangle on the New Bespeak tool, select Intersect Ii Objects, then click the circumference of both circles. Notice that ii points will appear in their intersections. Later on step 6, drawing should look like the one shown in Figure 2.

Figure 3 - Circles with radius AB and intersection C and D.

seven We only demand three points, points A, B and C, to form an equilateral triangle, so nosotros volition hide the ii circles, segment AB and indicate D. To do this, right click each object and click the Evidence Object option to uncheck it. In hiding segment AB, be sure that you practise not click points A or B.

8 With just three points remaining on the cartoon pad, click the Polygon tool and click the points in the post-obit order: indicate A, point B, point C and then point A to shut the polygon. Afterward pace 8, your drawing should wait like the figure beneath. Notation that in other versions, or depending on the setting, segment labels may announced.

Figure four - Triangle formed from radii of 2 circles

9 Using the Move button, move the vertices of the triangle. What do you lot notice? Notice that y'all tin can move vertex A and B but you can never motility vertex C. This is considering vertex C is a dependent object. Recall that vertex C is the intersection of ii circles and thus depends on the length of segment AB.

x Yous have probably observed that it seems that ABC is an equilateral triangle. In fact, information technology is. To verify, we tin display the interior angles of the triangle. To do this, click the Angle tool, and then click the interior of the triangle.

11 What practise you observe? Move the vertices of the triangle. Is your observation nevertheless the aforementioned?

12 You can also verify the length of the sides using the Properties window. To exercise this, right click one of the sides of the triangle, click Object Properties from the context menu.

thirteen In the Object Properties window, select the Basic tab. Be sure that the Testify label check box is checked and choose Value from the Show label driblet down list box.

14 Select the other sides of the triangle in the Object listing located at the left side of the Object Backdrop window and change the labels to Value, then shut the window when you lot are done.

15 Prove that the construction above always results to an equilateral triangle.

This tutorial is based on the GeoGebra Tutorial Series of Mathematics and Multimedia

Tutorial: Amalgam an Equilateral Triangle

es:Tutorial:Triángulo hasta Equilátero

Source: https://wiki.geogebra.org/en/Tutorial:EquilateralTriangle

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