Euclidean plane geometry
Pythagorean Theorem
Triangles
Subject:
There are 3 types of triangles including isosceles, scalene,and equilateral triangles. Triangles can be obtuse, acute, or right triangles. Some special measurements of a triangle are 30-60-90 and 45-45-90 triangles. Different ways can be used to find missing side lengths and angle measurements.
Inverses of Trigonometric Ratios
Subject:
Inverses of Trigonometric Ratios
You've learned how to use trig ratios to solve right triangles, finding the lengths of the sides of triangles. But what if you have the sides, and need to find the angles? You know that you can take side lengths and find trig ratios, and you know you can find trig ratios (in your calculator) for angles. What is missing is a way to go from the ratios back to the original angles. And that is what "inverse trig" values are all about.
If you look at your calculator, you should see, right above the "SIN", "COS", "TAN" buttons, notations along the lines of "SIN–1", "COS–1", and "TAN–1", or possibly "ASIN", "ACOS", and "ATAN". These are what you'll use to find angles from ratios.
the pythagorean therom
Subject:
The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:[1]
A^2+B^2=C^2
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
polygon notes
Subject:
polygons are closed objects with linear side
Geometry Cheat Sheet
Subject:
Theorems, Conjectures, & Postulates Triangle Theorems Triangle Sum Theorem- The sum of the measures of the angles in every triangle is 180? Exterior Angle Theorem- The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. Corollary to the Triangle Sum Theorem- In a right triangle, the acute angles are complementary. Base Angles Theorem ? If two sides of a triangle are congruent, then the angles opposite them are congruent. Converse of Base Angles Theorem ? If two angles of a triangle are congruent, the sides opposite them are congruent. Corollary to the Base Angle Theorem ? If a triangle is equilateral, then it?s equiangular.
Pythagorean Theorem
Subject:
Definition
The longest side of the triangle is called the "hypotenuse", so the formal definition is:
In a right angled triangle the square of the hypotenuse is equal to
the sum of the squares of the other two sides.
So, the square of a (a²) plus the square of b (b²) is equal to the square of c (c²):
a2 + b2 = c2
Sure ... ?
Let's see if it really works using an example. A "3,4,5" triangle has a right angle in it, so the formula should work.
Let's check if the areas are the same:
32 + 42 = 52
Calculating this becomes:
9 + 16 = 25
Yes, it works !
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