bankerboy30 wrote:
How are we getting different variables x and y when the sides are equal. Can you explain Krishna. Cause three sides are equal shouldn't their angles be noted with the same variable?
Note the sides that are equal
OC = AC = AB
OC and AC are sides if a triangle and the angles opposite to them are marked as x each (i.e. they are equal)
AC and AB are equal sides of another triangle and angles opposite to them are marked as y each. Note that you cannot mark them as x too because they are equal angles in a different triangle. Their measure could be different from x. I have explained this in detail in a post given below. Giving the explanation here:
"When two sides of a triangle are equal, the two opposite angles are equal. But can you say what the two angles are? No. Say a triangle has two sides of length 5 cm each. Do we know the measure of equal angles? No. They could be 40-40 or 50-50 or 80-80 etc. So if you have two different triangles with 2 sides of length 5 cm each, the equal angle could have different measures - in one triangle the equal angles could be 50-50, in the other triangle, the equal angles could be 70-70.
In triangle OAC, since OC = AC, you have two equal angles as x each. The third angle here is 180 - 2x.
In triangle ACB, since AC = AB, angle ACB = angle ABC but what makes you say that they must be x each too? This is a different triangle. Even if the sides have the same length as the sides of triangle OAC, there is no reason to believe that the equal angles need to be x each. So you call the angles y. The third angle here is 180 - 2y."
_________________
Karishma
Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >