12th March, 2012: How do we calculate the area of rectangles and triangles?

Area is defined as the number of square units that covers a closed figure. [iCoachMath]

You find the area of shapes like rectangles and triangles by using different formulas for both. For example, to find the area of a rectangle, you multiply the base times the height. For a triangle, there's a conjecture that says:

The area of a triangle is given by the formula A= 1/2(BxH), where A is the area, B is the base, and H is the height.

5th of March, 2012: How do we find the locus of points?

The locus is the set of all points that satisfy a given condition. It is a general graph of a given equation.

There are five locus theorems:

1. One point: A circle with the original point at its center.
2. Two fixed points: The locus of points equidistant from two points is the perpendicular bisector of the line segment connecting the two points
3. One line: the locus of points equidistant from a line are two lines, on opposite sides, and equidistant and parallel to that line
4. Two parallel lines: A line through the middle of the two lines
5. Two intersecting lines: Two intersecting lines half-way between the two original points

28th February, 2012: What is a mathematical statement?

A mathematical statement is a statement that can be judged to be true or false.

There are three types of mathematical statements:
A conditional: The most frequently used statement in the construction of an argument or in the study of mathematics.
Ex: If the two angles are congruent, then the two angles are both right angles.

An inverse: a conditional statement is formed by negating the hypothesis and negating the conclusion of the original statement. [Regents Prep]
Ex: If the two angles are not congruent, then the two angles are not right angles.

A contrapositive: Negating and switching the hypothesis and conclusion.
Ex: (Normal sentence): If Lisa sells her house, then her income did not stay the same.
Contrapositive: If Lisa's income stays the same, the she will not sell her house.