# Triangle FAQs:

Q: Is a triangle a polygon with three edges and three vertices?

A: Yes.

Q: Is a triangle a straight line through a vertex which cuts the corresponding angle in half?

A: Yes.

Q: Are triangles strong in terms of rigidity, but while packed in a tessellating arrangement triangles are not as strong as hexagons under compression?

A: Yes, Tessellated triangles still maintain superior strength for cantilevering however, and this is the basis for one of the strongest man made structures, the tetrahedral truss.

Q: Are triangles similar?

A: Yes.

Q: Is a triangle complementary?

A: Yes.

Q: Is a triangle the midpoints of the reference triangle's sides?

A: Yes, and so the pedal triangle is called the midpoint triangle or medial triangle.

Q: Is a triangle 360 degrees?

A: Yes.

Q: Is a triangle acute?

A: Yes, if the circumcenter is located outside the triangle, then the triangle is obtuse.

Q: Are triangles similar?

A: Yes.

Q: Are triangles all in the same proportion?

A: Yes, and then the triangles are similar.

Q: Are triangles sturdy?

A: Yes, while a rectangle can collapse into a parallelogram from pressure to one of its points, triangles have a natural strength which supports structures against lateral pressures.

Q: Are triangles permitted?

A: Yes, and angles of 0° are permitted.

Q: Is a triangle a straight line passing through the midpoint of the side and being perpendicular to it, i.e?

A: Yes, forming a right angle with it.

Q: Is a triangle the ellipse inscribed within the triangle tangent to its sides at the contact points of its excircles?

A: Yes.

Q: Is a triangle equal to the sum of the measures of the two interior angles that are not adjacent to it?

A: Yes, this is the exterior angle theorem.

Q: Are triangles right triangles with additional properties that make calculations involving them easier?

A: Yes.

Q: Are triangles assumed to be two-dimensional plane figures, unless the context provides otherwise?

A: Yes, In rigorous treatments, a triangle is therefore called a 2-simplex. Elementary facts about triangles were presented by Euclid in books 1–4 of his Elements, around 300 BC.

Q: Is a triangle acute?

A: Yes.

Q: Is a triangle often constructed by proving that three symmetrically constructed points are collinear: here Menelaus' theorem gives a useful general criterion?

A: Yes.

Q: Is a triangle a straight line through a vertex and perpendicular to the opposite side?

A: Yes.

Q: Are triangles said to be similar if every angle of one triangle has the same measure as the corresponding angle in the other triangle?

A: Yes.

Q: Is a triangle equilateral?

A: Yes.

Q: Is a triangle a triangle which is not contained in a plane?

A: Yes.

Q: Is a triangle determined by the lengths of the sides?

A: Yes.

Q: Is a triangle equilateral?

A: Yes.

Q: Are triangles osceles triangles?

A: Yes.

Q: Is a triangle an elementary problem encountered often in many different situations?

A: Yes.

Q: Are triangles congruent?

A: Yes.

Q: Is a triangle therefore equilateral?

A: Yes.

Q: Are triangles congruent because one triangle could be obtuse-angled and the other acute-angled?

A: Yes.

Q: Are triangles in the same proportion as are another pair of corresponding sides?

A: Yes, and their included angles have the same measure, then the triangles are similar.

Q: Is a triangle to place the triangle in an arbitrary location and orientation in the Cartesian plane?

A: Yes, and to use Cartesian coordinates.

Q: Is a triangle a straight line through a vertex and the midpoint of the opposite side?

A: Yes, and divides the triangle into two equal areas.

Q: Is a triangle an angle that is a linear pair to an interior angle?

A: Yes.