BC: THE END.
FC: Geometry scrapbook by mehribon kamolova
1: Table of contents Polygons...........................2&3 Midpoints..................4&5 Flowchart proof.................6&7 Inverse ,Converse,and Contrapositives............8&9 Slope.............................10&11 Properties of parallelograms........12&13 Planes.............14&15 Properties midsegment............16&17 Isosceles and Equilateral18&19 triangles.... Statement and truth values..............20&21..
2: POLYGONS | Polygons- A plane figure with at least three straight sides and angles, and typically five or more. Is it a Polygon? Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up). Polygon comes from Greek. Poly- means "many" and -gon means "angle". A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself! Many rules about polygons don't work when it is complex.
5: The Midpoint Formula 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. Think about it this way: If you are given two numbers, you can find the number exactly between them by averaging them, by adding them together and dividing by two. For example, the number exactly halfway between 5 and 10 is [5 + 10]/2 = 15/2 = 7.5. | Midpoints
6: Flowchart proof-A flow chart proof, sometimes called a flow proof, is a graphical way of showing the logical steps used to demonstrate some mathematical claim. For example, from some given information, the flow chart might show the various logical steps taken to prove that two triangles are congruent. | flowchart proof
7: Statements A flow chart proof is presented as a series of statements written in boxes. Each statement logically follows the ones before it. For example, a box may contain the statement that two line segments are congruent.
8: Inverse ,Converse,and Contrapositives
10: EXAMPLE- Find the slope of the line segment joining the points ( 1, - 4 ) and ( - 4, 2 ). Solution Label the points as x1 = 1, y1 = - 4, x2 = -4, and y2 = 2. To find the slope m of the line segment joining the points, use the slope formula : Example Solution So, m = - 6/5. | Slope-A surface of which one end or side is at a higher level than another.
12: A parallelogram is a quadrilateral with opposite sides parallel. It is the "parent" of some other quadrilaterals, which are obtained by adding restrictions of various kinds: A rectangle is a parallelogram but with all four interior angles fixed at 90 A rhombus is a parallelogram but with all sides equal in length A square is a parallelogram but with all sides equal in length and all angles fixed at 90 | Properties of Parallelograms
14: PLANES | 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). Properties Two planes are either parallel or they intersect in a line. A line is either parallel to a plane, intersects it at a single point in three-dimensional space, or is contained in the plane. Two lines perpendicular to the same plane must be parallel to each other. Two planes perpendicular to the same line must be parallel to each other.
16: Properties Midsegment 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. The midsegment of a trapezoid is parallel to the bases and is equal in length to the average of the lengths of the two bases. \ \ | PROPERTIES OF MIDSEGMENTS
18: Isosceles and Equilateral triangles. | An isosceles triangle has two congruent sides called legs and a third side called the base. The vertex angle is the angle included by the legs. The other two angles are called base angles. The base angles are congruent. The figure below depicts an isosceles triangle with all the parts labeled.
19: An equilateral triangle is a special isosceles triangle in which all three sides are congruent. Equilateral triangles are also equiangular, which means all three angles are congruent. The measure of each angle is 60 degrees. The figure below depicts an equilateral triangle with all the parts labeled.
20: STATEMENTS AND TRUTH VALUES