How many different kinds of triangles are there?

Question

Example: Some triangles have all equal sides.

Answer 1

You have asked a very interesting question.

There are three two dimensional geometries: Euclidean, spherical, and hyperbolic.

In Euclidean geometry, the sum of the angles of the triangle equal 180 degrees, in spherical the sum of the angles of the triangle exceeds 180 degrees, and in hyperbolic it is less than 180 degrees.

Triangles have a lot of properties--too many to list in a brief response. An outstanding reference that goes beyond what is covered in the typical high school geometry course is Posamentier's Advanced Euclidean Geometry text.

You can find more information regarding his text at

http://www.keypress.com/catalog/products/supplementals/Prod_AdvancedEuclidean.html

I have taught the course for 10 years and always rely on this text. It will teach you more about triangles than you thought there was to know about triangles! :) After you study Ceva and Menelaus, you'll know that you have learned some neat Euclidean geometry.

Answer 2

Triangles may be classified by the lengths of their sides and the measures of their angles.

In general:
Equilateral triangles have 3 congruent sides.
Isosceles triangles have at least 2 congruent sides. [Equilateral triangles are also isosceles.]
Scalene triangles have no congruent sides.
Acute triangles have 3 acute angles.
Right triangles have 1 right angle.
Obtuse triangles have 1 obtuse angle.

More specifically, triangles can be of 7 different classifications:
[1] Equilateral or Equiangular. [Each angle measures 60°.]
[2] Acute Isosceles. [The angles measure x°, x°, and (180 - 2x)°,
where 45° < x < 90°. In the case that x 60°, the triangle is also equiangular.]
[3] Right Isosceles. [The angles measure 45°, 45°, and 90°.]
[4] Obtuse Isosceles. [The angles measure x°, x°, and (180 - 2x)°,
where x < 45°.]
[5] Acute Scalene. [The angles measure a, b, and c, where a < b < c < 90°.]
[6] Right Scalene. [The angles measure a, b, and 90°, where a < b < 90°.]
[7] Obtuse Scalene [The angles measure a, b, and c, where a < b < 90° < c.]

Answer 3

In terms of classifying triangles, there are several ways of doing so. For example, acute triangles have all three angles less than 90 degrees. Right triangles have one right (90 degree) angle. Obtuse triangles have on angle greater than 90 degrees.

Or, there's scalene, where all three sides differ in length. Isoceles, where two of the three sides are equal, and all three sides equal is equilateral. It can be shown that equilateral triangles are also equiangular, there all three angles are the same.

Triangle can then be combinations of the above, such as a scalene right triangle. Not all are possible, since all equilateral triangles are acute.

Answer 4

There are 3 types of triangles as follows:

1 Acute angled triangle
2 Obtuse angled triangle
3 Right angled triangle.

When all sides are equal it is called equlateral triangle.

Answer 5

Triangles:

According to angles
oblique triangle = triangle with no right triangle
acute triangle = triangle with 3 acute angles (a kind of oblique triangle)
right triangle = triangle with 1 right angle
obtuse triangle = triangle with 1 obtuse angle ( a kind of oblique triangle)
Equiangular triangle = triangle with 3 congruent angles (under the acute triangle)

According to sides
Isosceles triangle = triangle with at least 2 congruent sides
Equilateral triangle = triangle with 3 congruent sides (also a special type of isosceles triangle)
Scalene triangle = triangle with no equal sides

^_^

Answer 6

Triangles are classified on two bases. There are 3 kinds of triangles according to the relation of their sides, namely:

equilateral triangle -having all of its sides equal in measures
isosceles triangle - having two of its sides equal in measures
scalene-having none of its sides equal

Triangle can also be classified according to the measure of its angles, namely

right triangle- having a right angle and two acute angles
obtuse triangle-having an obtuse angle and two acute angles
acute triangle- having 3 of its angles that are acute
One type of acute triangle having with all of its acute angles equal in measures is called EQUIANGULAR TRIANGLE

Answer 7

There are three different types of triangles, equilateral - all sides equal in length, isosceles - two sides of eqaul length, and scalene - all sides different lengths.

Triangles can also be defined by their largest angle. Right angle - one angle is 90 degrees, acute triangle - all angles less than 90 degrees, and obtuse triangle - largest angle over 90 degrees.

Answer 8

6

Answer 9

triangles can be classified based on the sides or based on the angles
on the basis of sides
1.when all the three so\ides are equal....equilateral triangle
2.when any two side are equal...............isosceles triangle
3.when no two sides are equal..................scalene triangle
on the basis of the angles
1.when all the angles are equal..equiangular triangle..(equiangular triangle will also be equilateral triangle.in this all the three angles will be 60 deg each)
2.when all the angles are acute..acute triangle or acute angled triangle
3.when any one angle is obtuse(there can be only one obtuse angle in a triangle)..obtuse triangle or obtuse angled triangle
4.when any one angle is a right angle(there can be only on right angle in a triangle)..right triangle or right angled triangle

Answer 10

Equilateral Triangle
Right Triangle
Other Triangles (with varying obtuse/acute angles)