# Triangles

The Altermundus packages have some helpful macros for working with triangles.
\tkzDrawPolygon[ options ]( list of points )  Define the 3 vertices of the triangle and then use this macro to create the triangle. As you can guess, this macro can form any polygon if you give the list of points in the order you want them connected.

\tkzDrawTriangle[ options ](A,B) Give the two vertices you want the triangle to have and set the options to create a triangle having the characteristics you want:

• two angles= #1 and #2: This will create the triangle having base angles of 1 and 2 and then determine where the third point has to be to achieve that triangle. Example: two angles=20 and 50
• equilateral: determines where the third point has to be to create an equilateral triangle.
• pythagore: creates a classic right triangle with sides of length 3,4, and 5.
• school: Creates a 30-60-90 right triangle
• gold: Creates a right triangle such that the ratio of the measurements of two sides adjacent to the corner right equals Φ = 1, 618034. See here. A is the peak.
• euclide: same as above but AB is the base of the triangle
• golden: the third vertex is determined so that AB / AC = Φ
• cheops: where C creates an isosceles triangle such that and AC / AB = Φ

Here is the output when the various options are used:

There are 3 very well known results for triangles:

• The angle bisectors of a triangle all intersect at a point called the incenter
• The medians of a triangle all intersect at a point called the centroid
• The altitudes of a triangle all intersect at a point called the orthocenter

The Altermundus package makes drawing those easy

\tkzDrawBisector(B,A,C) Draw a bisector of angle BAC, whether it's in a triangle or not.

\tkzDrawMedian[options](A,B)(C) Draw a median from side AB to vertex C

\tkzDrawAltitude[options](A,B)(C) Draw an altitude from side AB to vertex C

These can be illustrated with the following examples of their usage:

More Triangles

For creating typical triangles used in school we need three more macros:

\tkzGetPoint{name of point} will get the point created from a previous calculation. Example:

\tkzMarkAngle[options](pt1,pt2,pt3) will mark the angle created by the three points pt1, pt2, and pt3, where pt2 is the vertex of the angle. This is needed for creating congruent angle marks. The order of the points is important because one of the angles from \tkzMarkAngle[options](pt1,pt2,pt3) and \tkzMarkAngle[options](pt3,pt2,pt1) is an acute angle and the other is obtuse.The option arc=l or arc=ll or ... controls the number of tick marks used in marking the segment. Note that this is an "el" l, not a vertical bar |

\tkzMarkRightAngle(pt1,pt2,pt3) will create a right angle mark for the angled defined by the three points pt1, pt2, and pt3, where pt2 is the vertex of the angle. The order of the vertices is important as it is with \tkzMarkAngle.

\tkzMarkSegment[options](pt1,pt2) will mark the segment defined by pt1 and pt2. This is needed for creating congruent side marks. The option mark=| or mark=|| or ... controls the number of tick marks used in marking the segment.

\tkzLabelAngle[pos =.7](pt1,pt2,pt3){$60^{\circ}$} labels the angle created by pt1, pt2, and pt3 with the text $latex 60^{\circ}$ placed at position pos=.7 away from the angle.

One of the most useful macros for tkz-euclide is \tkzGetPoint (there are other macros \tkzGetPoints{M}{N}, \tkzGetFirstPoint{M}, and \tkzGetSecondPoint{N} as well) which can be used following other macros that result in some sort of calculation. In particular, the macro \tkzDrawTriangle[ options ](A,B) creates a triangle but congruent sides and angles can't be marked until we know the third vertex of the triangle. This was created when \tkzDrawTriangle[ options ](A,B) was called, so \tkzGetPoint will result in the third vertex of the triangle which can then be used. Here's a simple example:

\begin{tikzpicture}[scale=1]
%choose the vertices of the triangle
\tkzDefPoint(0,0){A}
\tkzDefPoint(1,3){B}
\tkzDrawTriangle[two angles=60 and 60](A,B)
\tkzGetPoint{C} %Gets the third vertex of the triangle
\tkzMarkAngle[fill=yellow, size=.8cm,opacity=.5](A,C,B)
\tkzMarkAngle[fill=green, size=.8cm,opacity=.5](C,B,A)
\tkzMarkAngle[size=.8cm,opacity=.5](B,A,C)
\tkzMarkSegment[color=red,pos=0.5,mark=|](A,B)
\tkzMarkSegment[color=red,pos=0.5,mark=|](C,B)
\tkzMarkSegment[color=red,pos=0.5,mark=|](A,C)
\end{tikzpicture}