How to construct special line segments in a triangle
The next two pages give detailed instructions on how to construct the special line
segments in a triangle that we worked on in class. It is hard to give clear
directions on how to do this without using a picture as a reference. Look in your
book on page 522 and 523 for detailed pictures – if you have any questions or
notice any mistakes, please email me.
(I) Median: a line segment drawn from a vertex to the side opposite the vertex;
the line segment intersects the side of the triangle at its midpoint – the point that
divides the side in half
-- To construct a median using a protractor, you must follow these steps:
• Measure the side of the triangle to which you are drawing a line segment
• Based on the measurement, divide the side of the triangle into 2 equal
pieces (in half)
• Now draw a line segment from the vertex opposite the side you
measured to the half-way point of the side
• Repeat this process for all 3 sides of the triangle.
• Note: Make sure to label your median correctly. It is a line segment and
therefore you must use correct notation. For example, you would say
_
something like AC is a median of triangle BAF .
(II) Angle bisector: a line segment drawn from a vertex that bisects (cuts the
angle into 2 equal pieces) the angle formed by that vertex.
-- To construct an angle bisector using a protractor, you must follow these steps:
• Measure the angle that you want to bisect (cut in half) with a protractor;
you will have to extend the lines of the triangle in order to get an accurate
measurement of the angle.
• Based on the measurement, divide the angle into 2 equal pieces.
• Now draw a line segment from the vertex to the point that you marked to
denote the 2 equal pieces of the angle.
• Repeat this process for all 3 angles of the triangle.
• Note: Make sure to label your angle bisector correctly. It is a line
segment and therefore you must use correct notation. For example, you
_
would say something like AC is an angle bisector of triangle BAF .
(III) Perpendicular bisector: a line drawn that goes through the midpoint of a
side of the triangle; the line drawn must be perpendicular to the side of the
triangle (i.e., the line forms a 90° angle at the midpoint).
-- To construct a perpendicular bisector using a protractor, you must follow these
steps:
• Measure the side of the triangle through which you want to draw the
perpendicular line.
• Based on the measurement, divide the side of the triangle into 2 equal
pieces.
• From the point on the side of the triangle that denotes the midpoint of
that side, form a right angle (use a protractor!) with the side of the triangle
being one side of the right angle. Make a mark where the other side of the
right angle will be.
• Using the 2 points you now have marked (the midpoint and where the
other side of the right angle will be), draw a line. This line is your
perpendicular bisector.
• Repeat this process for all 3 sides of the triangle.
• Note: Make sure to label your perpendicular bisector correctly. It is a line
and therefore you must use correct notation. For example, you would say

_
_
something like AC is an perpendicular bisector of side PN (where PN is
a side of the triangle).
(IV) Altitude: a line segment that is drawn from a vertex to the side of the
triangle opposite the vertex. This line segment is perpendicular (form a 90°
angle) with the side of the triangle opposite the vertex. NOTE: Some altitudes
may be drawn outside of the triangle, whereas some altitudes are just the sides
of the triangle itself.
-- To construct an altitude using a protractor, you must follow these steps:
• From the vertex that you want to draw an altitude from, draw a line
that is tangent to that vertex (line touches the triangle ONLY at the vertex)
and parallel to the side of the triangle opposite the vertex.
• Take a protractor and use that vertex as the vertex of your right angle
and the tangent line as one of the sides of your right angle. Make a mark
where the other side of your right angle will be.
• Using the 2 points you now have (the vertex and the one you made for
where the other side of the right angle will be),draw a line. This line is
your is your altitude.
• Repeat this process for all 3 vertices of the triangle.
• Note: Make sure to label your altitude correctly. It is a line segment and
therefore you must use correct notation. For example, you would say something
_
like AC is an altitude of triangle BAF .