list out the types of triangles based on ,a)by length of sides b)By internal angles
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See there are mainly four types of triangles
Isosceles triangle
Equilateral triangle
Scalene triangle
Right angled triangle By internal angles
Triangles can also be classified according to their internal angles, measured here in degrees.
A right triangle (or right-angled triangle, formerly called a rectangled triangle) has one of its interior angles measuring 90° (a right angle). The side opposite to the right angle is the hypotenuse, the longest side of the triangle. The other two sides are called the legs or catheti[4] (singular: cathetus) of the triangle. Right triangles obey the Pythagorean theorem: the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse: a2 + b2 = c2, where a and b are the lengths of the legs and c is the length of the hypotenuse. Special right triangles are right triangles with additional properties that make calculations involving them easier. One of the two most famous is the 3–4–5 right triangle, where 32 + 42 = 52. In this situation, 3, 4, and 5 are a Pythagorean triple. The other one is an isosceles triangle that has 2 angles that each measure 45 degrees.
Triangles that do not have an angle measuring 90° are called oblique triangles.
A triangle with all interior angles measuring less than 90° is an acute triangle or acute-angled triangle. If c is the length of the longest side, then a2 + b2 > c2, where a and b are the lengths of the other sides.
A triangle with one interior angle measuring more than 90° is an obtuse triangle or obtuse-angled triangle. If c is the length of the longest side, then a2 + b2 < c2, where a and b are the lengths of the other sides.
A triangle with an interior angle of 180° (and collinear vertices) is degenerate.
A right degenerate triangle has collinear vertices, two of which are coincident.
A triangle that has two angles with the same measure also has two sides with the same length, and therefore it is an isosceles triangle. It follows that in a triangle where all angles have the same measure, all three sides have the same length, and such a triangle is therefore equilateral.
Right triangle Obtuse triangle Acute triangle.
Similarity and congruence
Two triangles are said to be similar if every angle of one triangle has the same measure as the corresponding angle in the other triangle. The corresponding sides of similar triangles have lengths that are in the same proportion, and this property is also sufficient to establish similarity.
Some basic theorems about similar triangles are:
If and only if one pair of internal angles of two triangles have the same measure as each other, and another pair also have the same measure as each other, the triangles are similar.
If and only if one pair of corresponding sides of two triangles are in the same proportion as are another pair of corresponding sides, and their included angles have the same measure, then the triangles are similar. (The included angle for any two sides of a polygon is the internal angle between those two sides.)
If and only if three pairs of corresponding sides of two triangles are all in the same proportion, then the triangles are similar.[note 3]
Two triangles that are congruent have exactly the same size and shape:[note 4] all pairs of corresponding interior angles are equal in measure, and all pairs of corresponding sides have the same length. (This is a total of six equalities, but three are often sufficient to prove congruence.)
Some individually necessary and sufficient conditions for a pair of triangles to be congruent are:
SAS Postulate: Two sides in a triangle have the same length as two sides in the other triangle, and the included angles have the same measure.
ASA: Two interior angles and the included side in a triangle have the same measure and length, respectively, as those in the other triangle. (The included side for a pair of angles is the side that is common to them.)
SSS: Each side of a triangle has the same length as a corresponding side of the other triangle.a corresponding non-included angle of a triangle have the same length and measure, respectively, case of this criterion.
Hope it helps please give me a thanks
Isosceles triangle
Equilateral triangle
Scalene triangle
Right angled triangle By internal angles
Triangles can also be classified according to their internal angles, measured here in degrees.
A right triangle (or right-angled triangle, formerly called a rectangled triangle) has one of its interior angles measuring 90° (a right angle). The side opposite to the right angle is the hypotenuse, the longest side of the triangle. The other two sides are called the legs or catheti[4] (singular: cathetus) of the triangle. Right triangles obey the Pythagorean theorem: the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse: a2 + b2 = c2, where a and b are the lengths of the legs and c is the length of the hypotenuse. Special right triangles are right triangles with additional properties that make calculations involving them easier. One of the two most famous is the 3–4–5 right triangle, where 32 + 42 = 52. In this situation, 3, 4, and 5 are a Pythagorean triple. The other one is an isosceles triangle that has 2 angles that each measure 45 degrees.
Triangles that do not have an angle measuring 90° are called oblique triangles.
A triangle with all interior angles measuring less than 90° is an acute triangle or acute-angled triangle. If c is the length of the longest side, then a2 + b2 > c2, where a and b are the lengths of the other sides.
A triangle with one interior angle measuring more than 90° is an obtuse triangle or obtuse-angled triangle. If c is the length of the longest side, then a2 + b2 < c2, where a and b are the lengths of the other sides.
A triangle with an interior angle of 180° (and collinear vertices) is degenerate.
A right degenerate triangle has collinear vertices, two of which are coincident.
A triangle that has two angles with the same measure also has two sides with the same length, and therefore it is an isosceles triangle. It follows that in a triangle where all angles have the same measure, all three sides have the same length, and such a triangle is therefore equilateral.
Right triangle Obtuse triangle Acute triangle.
Similarity and congruence
Two triangles are said to be similar if every angle of one triangle has the same measure as the corresponding angle in the other triangle. The corresponding sides of similar triangles have lengths that are in the same proportion, and this property is also sufficient to establish similarity.
Some basic theorems about similar triangles are:
If and only if one pair of internal angles of two triangles have the same measure as each other, and another pair also have the same measure as each other, the triangles are similar.
If and only if one pair of corresponding sides of two triangles are in the same proportion as are another pair of corresponding sides, and their included angles have the same measure, then the triangles are similar. (The included angle for any two sides of a polygon is the internal angle between those two sides.)
If and only if three pairs of corresponding sides of two triangles are all in the same proportion, then the triangles are similar.[note 3]
Two triangles that are congruent have exactly the same size and shape:[note 4] all pairs of corresponding interior angles are equal in measure, and all pairs of corresponding sides have the same length. (This is a total of six equalities, but three are often sufficient to prove congruence.)
Some individually necessary and sufficient conditions for a pair of triangles to be congruent are:
SAS Postulate: Two sides in a triangle have the same length as two sides in the other triangle, and the included angles have the same measure.
ASA: Two interior angles and the included side in a triangle have the same measure and length, respectively, as those in the other triangle. (The included side for a pair of angles is the side that is common to them.)
SSS: Each side of a triangle has the same length as a corresponding side of the other triangle.a corresponding non-included angle of a triangle have the same length and measure, respectively, case of this criterion.
Hope it helps please give me a thanks
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Answer:
a) equilateral , isosceles , scalene
b) acute , obtuse , right
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