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samritamd
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4th edition Book 3: Geometry - Page 232 #5

by samritamd Mon Jan 05, 2015 7:45 pm

Could someone please explain why angle DFE is equal to angle CAE, which further makes letter A true? How come?
tommywallach
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Re: 4th edition Book 3: Geometry - Page 232 #5

by tommywallach Tue Jan 06, 2015 5:48 pm

Hey Samrita,

It's a little complicated, but it is all in the back. Here's what they say:

"Because DE is ½ of CE and FE is ½ of AE, and angle DEF is shared, then ACE and FDE must be similar"

Their point is this. Imagine all you could see here was the two lines that make up angle DEF (try drawing them). Now, if you "close off" the angle by turning it into a triangle, you create two new angles. In this case, that angle has been closed off TWICE. Once by DF and once by CA. We know that DF happens to cut the two lines (CE and AE) in EXACTLY half. If DF cut ONE of those lines in half, but hit SOMEWHERE else on the other line, then we would not know anything about the angles. But because it cut BOTH lines in half, then DF is parallel to CA, and these these triangles are now similar.

Does that make sense?

-t