Can a Triangle Be Scalene and Equiangular at the same time?

Question

My teacher asked that question on my hw. I'm not sure if its a trick question...

Answer 1

That is impossible..

Answer 2

The answer can easily be deduced from your question, and the answer is simply no, your teacher is only confusing you...
Based on:
»Theorem 4.1 (Isosceles Triangle Theorem)
Base angles of an isosceles triangle are equal.
- so even isosceles triangles cannot be equiangular.
»Corollary 4.6
An equilateral triangle is equiangular.
- this means that only equilateral triangles can have equal angles.
»Theorem 5.12 (Angle sum of a triangle)
The sum of the angles of a triangle equals a straight angle.
- A triangle has a sum of 180º, so if an equilateral triangle has equal angles, then it has 60º for each angle. Then if it is an isosceles triangle, then base angles are equal, so if the base angles have 70º each, then the vertex angle will have 40º. The scalene triangle has no sides equal, so it is impossible to have 3 equal angles, but a Scalene triangle can also be an Acute Triangle.


Hope this helps to enlighten you~!!

Answer 3

the answer is no

scalene is the type of triangle that doesn't fit into any of the other categories

equilateral triangle is one that is equal on all 3 sides and angles

isosceles is one that is equal on TWO sides (and hence angles) with the third one being different

scalene is one where the angles and sides are all of different lengths and don't include those with a right angle.

Answer 4

Never because equal angles lie opposite equal sides and being equiangular would mean equal sides which would mean not scalene.

Answer 5

No it cannot.

Scalene means to have three unequal lengthed sides.

Equiangular means to have the same angles on all sides. A triangles angles are always proportional to the length of the opposite side. Therefore, it is not possible.

Answer 6

You tell us

Answer 7

it's not possible, to have so.