Chapter 10: Constructions and Loci

A parallelogram with congruent diagonal is a ______.

These exploratory exercises can be done using a computer with a program that draws and measures geometric figures.

2. a. Draw any $▵ABC.$Draw the three medians. They should intersect in one point, as shown in the diagram at the right. Find the ratios $\frac{AG}{AD},\frac{BG}{BE},\frac{CG}{CF}.$ What do you notice?

Describe how you would construct each of the following:

The median of $\Delta ABC$ that contains vertex $B$.

On your paper, draw two segments roughly like those shown. Use these segments in Exercise $1-4$ to construct a segment having the indicated length. $3a-b$

Refer to the diagram in which the medians of a triangle are shown.

If $AB=6,$then $BP=?,AP=?$ .

Explain how you could construct a $30°$angle.

Is there some kind of triangle such that the perpendicular bisector of each side is also an angle bisector, a median, and an altitude?

Draw a figure roughly like one shown, but larger. Do the indicated construction clearly enough so that your method can be understood easily.

Draw a figure roughly like one shown, but larger. Do the indicated construction clearly enough so that your method can be understood easily.

Exercise $3$ suggests that you could construct other angles with certain measures. Name some.