Mathematics

• Geometry - comes from the greek word "geo" and "metron" which means "earth measurement". It is study of visual shapes, sizes, patterns, and positions
• Point :

  • Is a basic geometric concept.

  • All other geometric figures are made up of this(collection of this).

  • It is only idea in out mind.

  • It has only location but no size nor shape.

  • It can be modeled by a dot.

  • It is named using a capital letter.
• Line :

  • Is a continuous arrangement of infinitely many points.

  • Its length is infinite.

  • It extends infinitely in two directions.

  • It has no thickness.

  • It is named by a single lower case script letter of by any two points on a line. A line symbol is placed above the letters.
• Plane :

  • Is a flat surface that extends infinitely its length and width.

  • It is like an "infinite sheet of paper".

  • It has length and width but no thickness.

  • This is name by a single script capital letter or by any three points in this which are not in the same line.

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• Adjacent angles - two distinct angles with common vertex and common.
• Complementary angles - are two angles whose sum of measures equals 90°.
• Supplementary Angles - are two angles whose measures have the sum of 180°.
• Linear Pair - composed of two adjacent angles whose sum of the measure is 180° and the non-common sides.
• Vertical Angles - two nonadjacent angles formed by two intersecting lines. Vertical lines are congruent
• Parallel Lines - are lines that never meet no matter how long they will be extended, denoted by the symbol of "||".
• Intersecting Lines - are lines that exactly meet at one point.
• Perpendicular Lines - are lines that intersects at only one point and form four right angles, denoted by the symbol of "_|_"
• Polygons

  • Is a union of non-collinear segments.

  • The word "polygon" comes from the Greek word "poly" which means many and "gon" which means angles

  • Separates the plane into three sets of points:polygon itself,exterior, and in interior

  • Named hy writing their consecutive sides in order.
• Convex - no diagonal line is in the outside of the polygon.
• Concave - there is diagonal line in the outside of the polygon.
• Interior angles - are angles inside the polygon.
• Exterior angles - angle outside the polygon.
• Consecutive sides - are two sides that have common endpoint or vertex
• Consecutive angles - two angles whose vertices are on the same side
• Included side - common side of consecutive angles
• Included angle - angle containing the common vertex of two consecutive sides
• Diagonal - a segment joining non-consecutive vertices
• Equilateral - all sides are equal
• Equiangular - angles are all equal
• Regular - it it is both equilateral and equiangular
• Polygons classified according to sides:

  • Triangle

  • Quadrilateral

  • Pentagon

  • Hexagon

  • Heptagon

  • Octagon

  • Nonagon

  • Decagon

  • Undecagon

  • Dodecagon
• Properties of a Parallel lines cut by a Transversal:

  • Alternate interior angles

  • Alternate exterior angles

  • Corresponding angles

  • Interior/Exterior angles on the same side
• Circle - is a set of all points in a plane at a fixed distance from a given point called center. This is named by a center
• Radius - is a segment of a circle that joins the center and a point on the. Two or more radius are called "radii"
• Chord - is a segment whose endpoint lies on the circle
• Diameter - is a chord that passes through the center of the circle.
• Secant - is a line that intersects the circle in two
• Tangent - is a line that only intersect the circle at only one point called "Point of Tangency".
• Arc - of a circle is a part of circle from any of its points denoted by
• Minor Arc - is an arc of a circle that is less than a semicircle. It is named by two points in a capital letter
• Major Arc - is an arc of a circle that measures greater than semicircle. It is named using three capital letters ,two endpoints and one another point.
• Semicircle - is an arc that is half of the circumference of the circle.It is named using three capital letters ,two endpoints and another one point
• Central angle - of a circle is an angle whose vertex is at the center of a circle
• Inscribed angle - of a circle is an angle whose vertex is on the circle
• Angle Bisector - is a segment, ray, or a line that bisects an interior angle