Assignment #6:

By Jennifer Byrd

I began this exploration by constructing a triangle and it's midpoints using the program GSP. Then I constructed another triangle with the same length size as the midpoints. I will now explore the sketch and the relationship between the two triangles.

The large triangle is ABC and the smaller triangle is DEF.

I have reconstructed the small triangle with circles 3 different circles having radius of the line segments DE, EF, and DF.

First, I will determine if these triangles (ABC and DEF) are congruent. One way to tell if the two triangles will be congruent if the sides are of equal length. As you can see from the picture this will not be true but the angles are congruent.

Second, I will determine if these triangles are similar. One way to tell if the two triangles will be similar if the ratios of each side is equal and the angles are congruent.

mAB=6

mBC=4

mAC=2

Since,

mDE=3

mEF=2

mDF=1

Then the triangles are similar with congruent angles.

Now that we have proved that they are similar then we will determine if their area is similar as well.

A= 1/2 (b)(h)

Area(ABC)=4

Area(DEF)=1

These triangles are similar but by a greater ratio than the lengths. The ratio is 4/1=4. This makes sense if we take into account the fact that we are looking at a two-dimensional figure such as area. So the relationship is ratio^dim in this case is 2^2=4.