1st May, 2012: How do we use secant, chord, and tangent ratios in circles?

A secant in a circle is a straight line that intersects a curve at two or more points

A chord is a line segment on the interior of a circle with both points lying on the circle

Two chords intersect inside a circle. Segment A X segment B= segment C X segment D

If two secant segments intersect outside a circle, then the product of the secant segment with it's external portion equals he product if the other secant segments with it's external portion.

26th April, 2012: How do we review transformations?

Isometry: Length is preserved, the figures are congruent

There are 4 types of transformations:
Rotation

Dilation

Reflection

Translation

24th April, 2012: What are altitudes, perpendicular bisectors, and angle bisectors?

Review:

An angle bisector bisects an angle in half, creating two congruent angles.

A perpendicular bisector is a line segment that bisects a line, and it's perpendicular to that line, creating a right angle.

An altitude is the height of the triangle.

23rd April, 2012: What are properties of medians and centroids?

Review:

The median in a triangle is a line segment drawn from it's vertex (the very top) to the midpoint of it's opposite side. There are three medians in each triangle.

A centroid is the point of intersection of all its three medians.

19th April, 2012: How do we solve surface area and volume problems?

Review:
Area of a triangle: A= (BH/2) X2

Area of a kite: A= D1 (diagonal 1) X D2 (diagonal 2) /2


Given a semi-circle within a triangle, to find the area of the shaded region, you'd find the area of the triangle, area of the circle, then divide by two (since its a semi-circle). Then, you'd subtract the area of the circle from the triangle.

18th April, 2012: How do you find the surface area and volume of a sphere?

Spheres:

A sphere is the set of all points in space equidistant from a given point called the center.

You can find the surface area of a sphere by using the formula SA= 4πr².

Example: Given radius= 14inches

               SA= 4πr²

               SA= 4π(14)²

               SA= 784π

               SA= 2,463.0inches²

You can find the volume of a sphere by using the formula V= 4/3πr³.

Example: Given radius= 12meters

               V= 4/3πr³

               V= 4/3π(12)³

               V= 7,238.2meters³

15th March, 2012: How do we find the area of parallelograms, kites, and trapezoids?

Area of a parallelogram: B(ase) x H(eight)
Area of a trapezoid: (B1+B2/2)x H

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.

1st February, 2012: How do we identify transformations?

A transformation is when you move a geometric figure.
There are four different types of transformations.

A translation is when every point is moved the same distance in the same direction. For example:

A rotation is when a figure is flipped over a line of symmetry:

A reflection is when a figure is when a figure is turned around a single point:

A dilation is an enlargement or reduction in the size of an image: