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I need some Geometry help with Triangles.
Name the three triangles that are classified by their sides. Name the four triangles that are classified by their angles. Find the sum of the measures of the three interior angles of any triangle. Find the sum of the two acute angles of a right triangle.
Thanks..its for the Math-A-Thon
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The 3 classifications of triangles by their sides are:
equilateral: all three sides are the same
isosceles: two sides are the same
scalene: no sides are the same -- all 3 are different lengths
Triangles are also classified by 3 types of angles:
acute: an acute angle is less than 90 degrees. EVERY triangle has at least 2 acute angles. In an acute-angled triangle, ALL 3 angles are acute.
obtuse: an obtuse angle is more than 90 degrees. An obtuse- angled triangle has ONE obtuse angle.
right: a right angle is exactly 90 degrees. A right-angled triangle has ONE right angle.
NOTE: there is also an equiangular triangle: all 3 angles the same -- every equilateral triangle is also equiangular, and vice versa. An equiangular triangle is also an acute-angled triangle.
The sum of the 3 angles of EVERY triangle is 180 degrees.
Since a right triangle has ONE angle than is 90 degrees, the sum of the remaining two angles is 180 - 90 = 90 degrees.
The types of triangles classified by their sides are as follows:
1) Scalene- a triangle with no congruent sides. Congruent sides are the legs of a triangle that are of equal length.
2) Isosceles- a triangle with two congruent sides.
3) Equilateral- a triangle with three congruent sides.
The four types of triangles classified by their angles are as follows:
1)Acute- all interior angles measure less than 90 degrees
2)Right- one interior angle is 90 degrees
3)Obtuse- one interior angle measures more than 90 degrees
4)Equiangular- all interior angles are equal.
Unless you are using non Euclidean geometry (Not to worry, you are using Euclidean geometry.) the sum of the interior angles of any type of triangle is ALWAYS 180 degrees.
Since we know that the sum of the interior angles of any triangle equals 180 degrees, we can find the sum of the acute angles of a right triangle by simple subtracting what we know (a right triangle has an angle equal to 90 degrees) from the total.
where (a+b) is equal to the sum of the acute angles of any right triangle
The three types of triangles is isosceles, equilateral and scalene triangle. Isosceles triangle is a triangle that has two sides which are same in length. Equilateral triangle is a triangle that has all three sides the same length. Scalene triangle is a triangle that has no equal sides, all three sides have different lengths.
Triangles can also be classified by their angles itself. Acute means the triangle has an angle that is less than 90 degrees. Obtuse means that the triangle has an angle that is more than 90 degrees. Right angle means the angle is 90 degrees. Equiangular angle means all angles inside triangle is the same, just like an equilateral triangle. There is also a reflex angle, which is more than 180 degress but less than 360 degrees.
The sum of all interior angles in an triangle adds up to 180 degrees. A+B+C=180 (sum of angles in a triangle)
The sum of two interior angle in an right-angled triangle is 90 degrees. Since the first angle is already 90 degrees, the remaining interior angles would be 180-90= 90 degrees.
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