Question on Triangles

[rohansingal]

Hi,

I have a question regarding triangles/angles?

If a triangle has one angle that is 50 degrees and another angle that is 25 degrees, will the side opposite the 50 degree angle be twice as long as the side opposite the 25 degree angle?

Best,
Rohan

[Ben Ku]

Rohan,

The ratio of angles in a triangle HAS NO RELATIONSHIP WITH the ratio of the lengths of sides. The only thing we know is that the side opposite the largest angle is the longest side, and the side opposite the smallest angle is the shortest. Other than that, we cannot generalize the lengths.

[rohansingal]

Hi,

That makes sense. However, let's say there is a right triangle that is bisected and made into two right triangles. Will the 90 degree angle that has been bisected always be made into two 45 degree angles? ------- the specific question I am referring to is #19 on the Geometry Question Bank below (pic not shown).

If angle BAD is a right angle, what is the length of side BD?

(1) AC is perpendicular to BD

(2) BC = CD


Thanks,
Rohan

[Ben Ku]

Hi Rohan,

I think the problem is addressed in a couple of places:

http://www.manhattangmat.com/forums/mgmat-geometry-question-bank-t3502.html

http://www.manhattangmat.com/forums/perpendicular-bisector-of-isosceles-triangle-t594.html

Basically, the definition of bisecting an angle means cutting it in half, so if you bisect a 90 degree angle, each angle will be 45 degrees

Let me know if that makes sense, and if you have additional questions.