Question

which Two labels could you place on a Triangle with no sides equal in length and one obtuse angle? 1 obtuse and acute 2 obtuse and right 3 obtuse and scalene 4 obtuse and isosceles 5 obtuse and equilateral

Answer 1

Answer: 3, "obtuse and scalene".

Step-by-step explanation:

Equilateral has all sides equal, eliminate 5.

Isosceles has two sides equal, eliminate 4.

Haven't seen the word scalene since 1966...

Sum of angles is 180°, right angle is 90°, obtuse angle is more than 90°, so there is no such thing as a right and obtuse triangle, eliminate 2. Think |_/.

Similarly, only one angle can be obtuse, think \_/, so every obtuse triangle has two acute angles. But I'm pretty sure "acute triangle" is defined to exclude triangles with an obtuse angle. In that case, "obtuse and acute" is contradictory. Eliminate 1.

That leaves 3, "obtuse and scalene." So now I remember a scalene triangle is one with all three sides different.

Wondering if that means all three angles are different. Yes, because if two angles are equal, the triangle has to be isosceles with base between the equal angles, roughly /_\, so two sides are equal.