Math Is Fun Forum

finally

Guest

help please

Points $D$, $E$, and $F$ are the midpoints of sides $\overline{BC}$, $\overline{CA}$, and $\overline{AB}$ of $\triangle ABC$, respectively, and $\overline{CZ}$ is an altitude of the triangle. If $\angle BAC = 71^\circ$, $\angle ABC = 39^\circ$, and $\angle BCA = 70^\circ$, then what is $\angle EZD+\angle EFD$ in degrees?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: help please

Please use

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: help please

hi finally,

Welcome to the forum.

That circle is called the nine-point-circle of ABC.  It goes through D, E, F and Z.

So EFD = EZD.

My software Sketchpad labels the points in alphabetical order so the point Z shows up as G. 
I changed it on the diagram but forgot to alter the measurement statement m<MGD to m<MZD. 
It's 70 whatever you call it.

I've got a proof somewhere which I'll research if you post back.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob