## Show that a triangle is right angled

For the discussion of math. Duh.

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kaloyan_kolev
Posts: 1
Joined: Sat Apr 20, 2019 12:31 pm UTC

### Show that a triangle is right angled

In △ABC (not isosceles) CH, CL and CM are respectively height, bisector and median. Show that ∠ACB=90 degrees if and only if ∠HCL=∠MCL.

I think that I have to show that △MCB (or △ACM) is isosceles, but I can't figure it out. I will be very grateful if you help me.

Qaanol
The Cheshirest Catamount
Posts: 3069
Joined: Sat May 09, 2009 11:55 pm UTC

### Re: Show that a triangle is right angled

Height of what, bisector of what, and median of what?

Try drawing a picture.

Is this homework?
wee free kings

ucim
Posts: 6819
Joined: Fri Sep 28, 2012 3:23 pm UTC

### Re: Show that a triangle is right angled

Assuming H, L, and M are on segment AB (which is the only way to make sense of the question), ask yourself the following questions:

1: Sum of ∠A, ∠B, and ∠C is.... what?
2: What does that imply if (as desired) ∠C = 90 degrees?
3: Considering all the angles at C (except ∠ACB)... what is their sum?
4: Consider the consequences of the congruent angles of the two triangles you suspect must be isosceles.

That should get you going.

Jose
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