Math Is Fun Forum

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

triangles!!!

Triangle ABC is a right triangle with right angle at A. Suppose AX is an altitude of the triangle, AY is an angle bisector of the triangle, and  AZ is a median of the triangle, and angle XAY=13. If X  is on BY, then what is the measure of angle ZAC?

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I see you have graph paper.
You must be plotting something

Bob

Administrator

Registered: 2010-06-20

Posts: 10,646

Re: triangles!!!

hi cooljackiec

I assumed that Y and Z are on the line BC.

Because Z is the midpoint of BC and there is a right angle at A, Z is the circumcentre of ABC.  ie.  A circle centred on Z will go through A, B and C.

So ZA = ZC and ZAC is isosceles.

So work oiut angles in this order:

XAY
XYA
YAC
ZCA (= YCA)
ZAC

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: triangles!!!

An alternative way to work it out is:
XAY
YAB
XAB
XBA
ZAC (=ZCA)

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cooljackiec

Member

Registered: 2012-12-13

Posts: 186

Re: triangles!!!

oh yea, isoceles triangles! median of hypotenuse = half of hyptenuse. i get it

I got 32. not sure, this seems incorrect

Last edited by cooljackiec (2013-04-30 11:24:27)

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I see you have graph paper.
You must be plotting something

Bob

Administrator

Registered: 2010-06-20

Posts: 10,646

Re: triangles!!!

That's good.  32 is my answer too.

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