Is the triangle ABC, right angled at B?

Is the triangle ABC, right angled at B?

(1) Two interior angles of the triangle ABC are complementary.

Telling us that two angles = 90 while the third must also equal 90, but this makes no mention of which angles = 90 meaning B may or may not = 90. Insufficient.

(2) In the triangle ABC the length of the median drawn on side AC is shorter than the median drawn on side AB or BC.

The shortest median is drawn from the longest side to the opposite angle. Therefore, the angle opposite side AC is the longest but we still don't know it's measurement. The angle could be 80 while the other two angles are 40 and 60 respectively. Insufficient.

1+2) We know that the longest side is opposite side AC (i.e. angle B). We are also told that two angles are complementary (i.e. add up to 90.) This is important. The longest angle cannot be complementary because if it was, it would add up to 90 with another angle with the third angle having to = 90 which is impossible because it isn't the largest angle in the triangle. Angle B must = 90 on it's own while the other two angles = 90 together. Thus, the triangle is right at 90 degrees. SUFFICIENT

Bunuel First of all thanks for the explanation.Now I'm just asking out of the curiosity that can you post any prove of the second statement: " the shortest of the medians of the triangle is the one drawn to the longest side".

It's a known property and you can prove this yourself just be drawing triangles.

Hello pal,
In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it. Now you can try drawing it.

This question is a bit tricky because one tends to assume triangle ABC to be a right angle triangle.

The answers here are amazing and noteworthy!!!

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.