Assignment #4Nicole MostellerEMAT 6680Begin with acuteAssignment #4: Investigation #8.DABC. ConstructDMIGandDFDE(see instructions below). ProveDMIGis congruent toDFDE.Figure 1.

Figure 2.

How do the sides of DMIG relate to the sides of DABC?

Because the vertices
of **DMIG**
are all midpoints of **DABC**, **DMIG** is a medial triangle whose sides are
midsegments of **DABC**. Since the sides are midsegments, we
can conclude:

. to see why the midsegment is half the length of its corresponding side.Click here!

Figure 3.

__How do the sides
of DFDE
relate to the sides
of DABC?__

To see this relation, it is necessary to use the smaller triangles that have the common vertex H(DBCH,DABH, andDCAH. InDBCH, notice that pts.EandDare midpoints of two of its sides. This means that segmentEDis a midsegment ofDBCH, and . InDABH, pts.FandEare midpoints of two of its sides. By definition, segmentEFis a midsegment ofDABH, and . InDCAH, pts.FandDare midpoints of two of its sides. By definition, segmentFDis a midsegment ofDCAH, and .

Let's compile the conclusions made onFigure 2andFigure 3.

Using the transitive property, we can now conclude : MI = FDIG = DEGM = EF. By SSS,DMIGis congruent toDFDE.

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