Congruent triangles

• Apr 7th 2009, 03:32 AM
sammy28
Congruent triangles
hi all attached is a question and answer from an exam paper which i am having trouble with.

firstly i do not see how they can state the ASA rule without further information.

secondly i would have drawn the perpendicular bisector of line YZ and labelled the point of intersection with YZ as W then stated

YW = WZ (common)
XW (common)
XY=XY (given XYZ isoscles triangle)

therefore triangle congruent SSS

• Apr 7th 2009, 10:18 AM
Quote:

Originally Posted by sammy28
hi all attached is a question and answer from an exam paper which i am having trouble with.

firstly i do not see how they can state the ASA rule without further information.

secondly i would have drawn the perpendicular bisector of line YZ and labelled the point of intersection with YZ as W then stated

YW = WZ (common)
XW (common)
XY=XY (given XYZ isoscles triangle)

therefore triangle congruent SSS

For the first thing -What more information were you expecting, can you be little specific

Second thing-You have proved that YXW is congruent to ZXW
I guess you wanted to add some more --
Can you be a little more specific

Are you trying to find the ways of proving it other than those given (Smirk)
• Apr 7th 2009, 12:12 PM
sammy28
thanks ardash, i made a mistake in proving wrong triangles congruent (Itwasntme)

if you label the intersection of segments NZ and YM, O; then
for ASA to work i am thinking that angle ZYM = angle ZYX/2. but without extra given angles such as the angle at YNZ and the angle OYN or the angle YOZ then i dont see how to prove.

even if i were to draw a circle radius OY centre O then extend line segment YM to the circumferance i get the circle thm. ' the angle of a semi circle is a right angle', but this is no use to this problem.
• Apr 7th 2009, 12:39 PM
running-gag
Hi

You want to prove that triangles YMZ and ZNY are congruent using ASA rule.

It means that you need to show that :
1) angle NYZ = angle MZY
2) angle NZY = angle MYZ
3) side YZ = side YZ

1) triangle XYZ is isosceles with XY = XZ therefore angle XYZ = angle XZY
But N is on the segment [XY] therefore angle XYZ = angle NYZ
and M is on the segment [XZ] therefore angle XZY = angle MZY
Therefore angle NYZ = angle MZY

2) is given by construction of M and N

3) is of course evident

ASA rule shows that triangles YMZ and ZNY are congruent
• Apr 7th 2009, 01:44 PM
sammy28
thanks rg. i see my mistake now you point it out so clearly (Hi)