Chapter 10: Constructions and Loci
Draw a figure roughly like one shown, but larger. Do the indicated construction clearly enough so that your method can be understood easily.
The perpendicular to at .
Explain how to construct a triangle that is congruent to .
Draw, if possible, a triangle in which the perpendicular bisectors of the sides intersect in a point with the location described.
- A point inside the triangle
- A point outside the triangle
- A point on the triangle
A median of a triangle is a segment from a vertex to the _____ of the opposite side.
These exploratory exercises can be done using a computer with a program that draws and measures geometric figures.
1. Draw any Draw the bisectors of the angles of the triangle. They should intersect in one point. Draw a perpendicular segment from this point to each of the sides. Measure the length of each perpendicular segment. What do you notice?
On your paper, draw two segments roughly like those shown. Use these segments in Exercise to construct a segment having the indicated length.
Suggest an alternate procedure for Construct that uses Constructions and .
The construction of the following triangle whose sides are in the ratio .
Repeat Exercise , but use the method.
Construct an angle with the indicated measure.