Respuesta :
A triangle is a plain figure with three straight sides and three angles.
A triangle is a three sided, two dimensional shape. It has three angles which total to 180, as well as three vertices. Triangles can come in six total variations.
Angle Variations:
The first is an acute triangle, which is a triangle with angles less that 90 degrees. The second is the obtuse triangle, which includes one obtuse angle (an angle with more than 90 degrees), and two acute angles. The third is the equilateral triangle, which has three angles that equal 60 degrees.
Side Variations
The first is a scalene triangle, in which all of its sides are not equal to each other. The second is the isosceles triangle, which has two congruent sides, and a third side which is not congruent. The final triangle is an equilateral triangle, which, like the angle variation, has all of its sides being congruent.
Some important things to know:
Area:
A=1/2bh where b is the base and h is the height
Side Inequality
Determines if a triangle with certain side lengths is possible to create. States that a + b > c, a + c > b, and b + c > a. If all of those conditions are true, then the triangle is possible to create. However, if you are given a triangle with all the side lengths, you can take the two sides with the least value, and compare it with the third side and check if it is greater. If so, the triangle is possible, otherwise, it is not (For example, a triangle with sides 2, 3, and 2 is possible because 2 + 2 > 3. However, a triangle with side lengths 3, 5, and 1 is not possible because 3 + 1 is not greater than 5).
Trigonometric:
(Opp = opposite side, Hyp = Hypotenuse, Adj = Adjacent, side)
Sin = Opp/Hyp
Cos = Adj/Hyp
Tan = Opp/Adj
Law of Sines
[tex] \frac{sinA}{a} = \frac{sinB}{b} = \frac{sinC}{c} [/tex]
Law of Cosines
[tex]a^2 = b^2+c^2 - 2bc * cosA \\ b^2 = a^2+c^2 - 2ac * cosB \\ c^2 = a^2+b^2 - 2ab * cosC [/tex]
Finding area with Sine
[tex]A = \frac{1}{2} bc * sinA[/tex]
Pythagorean Theorem
[tex]a^2 + b^2 = c^2[/tex]
If I've left anything out you need to know in particular, please ask, and I'll try to help you out.
:)
Angle Variations:
The first is an acute triangle, which is a triangle with angles less that 90 degrees. The second is the obtuse triangle, which includes one obtuse angle (an angle with more than 90 degrees), and two acute angles. The third is the equilateral triangle, which has three angles that equal 60 degrees.
Side Variations
The first is a scalene triangle, in which all of its sides are not equal to each other. The second is the isosceles triangle, which has two congruent sides, and a third side which is not congruent. The final triangle is an equilateral triangle, which, like the angle variation, has all of its sides being congruent.
Some important things to know:
Area:
A=1/2bh where b is the base and h is the height
Side Inequality
Determines if a triangle with certain side lengths is possible to create. States that a + b > c, a + c > b, and b + c > a. If all of those conditions are true, then the triangle is possible to create. However, if you are given a triangle with all the side lengths, you can take the two sides with the least value, and compare it with the third side and check if it is greater. If so, the triangle is possible, otherwise, it is not (For example, a triangle with sides 2, 3, and 2 is possible because 2 + 2 > 3. However, a triangle with side lengths 3, 5, and 1 is not possible because 3 + 1 is not greater than 5).
Trigonometric:
(Opp = opposite side, Hyp = Hypotenuse, Adj = Adjacent, side)
Sin = Opp/Hyp
Cos = Adj/Hyp
Tan = Opp/Adj
Law of Sines
[tex] \frac{sinA}{a} = \frac{sinB}{b} = \frac{sinC}{c} [/tex]
Law of Cosines
[tex]a^2 = b^2+c^2 - 2bc * cosA \\ b^2 = a^2+c^2 - 2ac * cosB \\ c^2 = a^2+b^2 - 2ab * cosC [/tex]
Finding area with Sine
[tex]A = \frac{1}{2} bc * sinA[/tex]
Pythagorean Theorem
[tex]a^2 + b^2 = c^2[/tex]
If I've left anything out you need to know in particular, please ask, and I'll try to help you out.
:)
