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.
Show that a triangle is right angled
Moderators: gmalivuk, Moderators General, Prelates

 Posts: 1
 Joined: Sat Apr 20, 2019 12:31 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?
Try drawing a picture.
Is this homework?
wee free kings
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
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
Order of the Sillies, Honoris Causam  bestowed by charlie_grumbles on NP 859 * OTTscar winner: Wordsmith  bestowed by yappobiscuts and the OTT on NP 1832 * Ecclesiastical Calendar of the Order of the Holy Contradiction * Heartfelt thanks from addams and from me  you really made a difference.
Who is online
Users browsing this forum: No registered users and 27 guests