S: Geometry Scrapbook
BC: The End
FC: Geometry Scrap Book
1: Sometimes you need to find the point that is exactly between two other points. For instance, you might need to find a line that bisects (divides into equal halves) a given line segment. This middle point is called the "midpoint". The concept doesn't come up often, but the Formula is quite simple and obvious, so you should easily be able to remember it for later. The Midpoint Formula works exactly the same way. If you need to find the point that is exactly halfway between two given points, just average the x-values and the y-values.
2: A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), namely a cyclically ordered set of points in a plane, with no three successive points collinear, together with the line segments joining consecutive pairs of the points. In other words, a polygon is closed broken line lying in a plane"
3: There are several different angles associated with circles. Perhaps the one that most immediately comes to mind is the central angle. It is the central angle's ability to sweep through an arc of 360 degrees that determines the number of degrees usually thought of as being contained by a circle.
4: A circle is a simple shape of Euclidean geometry that is the set of all points in a plane that are a given distance from a given point, the center. The distance between any of the points and the center is called the radius. Mathematician: Pi r squared Baker: No! Pies are round, cake are squared!
5: Arcs An arc of a circle is a continuous portion of the circle. It consists of two endpoints and all the points on the circle between these endpoints. The symbol is used to denote an arc. This symbol is written over the endpoints that form the arc. There are three types of arcs: Semicircle: an arc whose endpoints are the endpoints of a diameter. It is named using three points. The first and third points are the endpoints of the diameter, and the middle point is any point of the arc between the endpoints. Minor arc: an arc that is less than a semicircle. A minor arc is named by using only the two endpoints of the arc. Major arc: an arc that is more than a semicircle. It is named by three points. The first and third are the endpoints, and the middle point is any point on the arc between the endpoints.
6: If the measures of two angles sum up 180, they are called supplementary angles. Each of a pair of supplementary angles is called a supplement of the other. | If the measures of two angles sum up 90, they are called complementary angles. Each of the two complementary angles is called a complement of the other.
7: An isosceles triangle is a triangle with (at least) two equal sides. In the figure to the left, the two equal sides have length and the remaining side has length . This property is equivalent to two angles of the triangle being equal. An isosceles triangle therefore has both two equal sides and two equal angles. The name derives from the Greek iso (same) and skelos (leg). | A triangle with all sides equal is called an equilateral triangle, and a triangle with no sides equal is called a scalene triangle. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides and angles equal. Another special case of an isosceles triangle is the isosceles right triangle.
8: Triangles, a three sided figure that has three angles and the total of three angles must add up to 180 degrees. Now, there are different types of triangles, they are called equilateral, isosceles, and scalene.
9: The sum of all angles in a triangle should always add up to 180 degrees and specific degrees have special names. 90 Degrees - Right < 90 Degrees - Acute Angle > 90 Degrees - Obtuse Angle
10: In mathematics, a plane is a flat, two-dimensional surface. A plane is the two dimensional analogue of a point (zero-dimensions), a line (one-dimension) and a solid (three-dimensions). | A plane may be considered as an infinite set of points forming a connected flat surface extending infinitely far in all directions. A plane has infinite length, infinite width, and zero height (or thickness). It is usually represented in drawings by a four-sided figure. A single capital letter is used to denote a plane.
11: In this special situation, the angles that are related are usually called vertical, or alternate exterior/interior. | Alternate and interior angles sort of behave like vertical angles, theres just a lot more of them and they usually occur when a transversal cuts two parallel lines.
12: Equilateral triangles means that the triangle contains all equal sides and equal angles. Figures to the right are used to show their conjectures and how they appear in math.
13: Scalene triangles are triangles where each side is a different length. They are unusual in that the are defined by what they are not. Most triangles drawn at random would be scalene. The interior angles of a scalene triangle are always all different. The converse of this is also true - If all three angles are different, then the triangle is scalene, and all the sides are different lengths.
14: Right triangles are like any other triangles, except their angle measures. One side is 90 degrees and the other two sides are congruent, 45 degrees. To the right are figures showing the right triangle and its conjectures.
15: One of the most important properties of a straight line is in how it angles away from the horizontal. This concept is reflected in something called the "slope" of the line
16: A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle. This segment has two special properties. It is always parallel to the third side, and the length of the midsegment is half the length of the third side.
17: A shape, formed by two lines or rays diverging from a common point (the vertex) | Like said before, there are different types of angles.
18: The method of solving "by substitution" works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable.
19: A quadrilateral is a shape that contains four sides and have to be two dimension. There are many types of quadrilaterals such as, squares, rectangles, rhombuses, and trapezoids. Pretty much if you connect four lines, and they all intersect, it is considered as a quadrilateral.
20: Intercepted arc: Corresponding to an angle, this is the portion of the circle that lies in the interior of the angle together with the endpoints of the arc. | Inscribed angle: In a circle, this is an angle formed by two chords with the vertex on the circle.
21: A chord of a circle is a geometric line segment whose endpoints both lie on the circle. A secant or a secant line is the line extension of a chord.