The Amazing-ness of Circles

Some things to remember about circles and properties of circles:




Keep in mind: A central angle is an angle whose vertex is the center of a circle. An arc is an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them.



Keep in mind that we just learned this chapter, and it is pretty fresh in my mind, so if I keep my comments to a bare minimum, you will know why. The circle information is pretty easy to understand, it's getting the hang of some of the problems that could be possibly difficult to some.





An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. An intercepted arc consists of endpoints that lie on the sides of an inscribed angle and all the points of the circle between them. A chord or arc subtends an angle if its endpoints lie on the sides of the angle.






Here is some information retained in chapter 11-5:





Entering into 11-6...


A secant segment is a segment of a secant with at least one endpoint on the circle. An external secant segment is a secant segment that lies in the exterior of the circle with one endpoint on the circle.



A tangent segment is a segment of a tangent with one endpoint on the circle. AB and AC are tangent segments.



The major formula from 11-7:


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Quadrilaterals and Everyday Life

It is fairly simple to spot quadrilaterals in everyday life, considering it's any four sided polygon. Anything that has a rectangle, square, rhombus, trapezoid, or kite shape is game. Try finding these shapes around your house, for instance right now I am looking at my wipe-off board, which is rectangle shaped, which is next to my sticky notes, which are square shaped. There is in fact a kite in my room, rather a drawing of one, and my boom box is trapezoid shaped (seriously, it is). There is even a rhombus shaped basket in my room (it's not usually there though, I don't know why it is there now). Go ahead and try it and see what you can find. These geometric shapes might surprise you.


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Similarities and Differences of Different Types of Quadrilaterals

A quadrilateral is a four-sided polygon. There are irregular and regular quadrilaterals.

A type of special quadrilateral is a rectangle. A rectangle is a quadrilateral with four right angles.

A rhombus is another special quadrilateral. A rhombus is a quadrilateral with four congruent sides.

A square is a quadrilateral with four right angles and four congruent sides.

Since these parallelograms are considered special, it is good to note that they have different sets of theorems and postulates that come with them.




A kite is a quadrilateral with exactly two pairs of congruent consecutive sides.



A trapezoid is a quadrilateral with exactly one pair of parallel sides. Each of the parallel sides is called a base. The nonparallel sides are called legs. Base angles of a trapezoid are two consecutive angles whose common side is a base.



The midsegment of a trapezoid is the segment whose endpoints are the midpoints of the legs.

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Entering Into Polygons

Remember that all the sides are congruent in an equilateral polygon. All the angles are congruent in an equiangular polygon. A regular polygon is one that is both equilateral and equiangular. If a polygon is not regular, it is called irregular.

A polygon is either concave or convex.





Remember the Polygon Angle Sum Theorem:


And the Polygon Exterior Angle Sum Theorem:


Always remember that any polygon with four sides is a quadrilateral. However, some quadrilaterals have special properties. These special quadrilaterals are given their own names.

Here are some properties of parallelograms:



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It is always important to note these theorems, mostly considering they are the bulk of what you will need to remember come test or quiz time, and like I said, I am a visual learner, so for me, this picture set up is golden.

Properties of Right Triangles that Allow Us to Analyze Figures

Note: this information about to be shown is VERY important. It will be mentioned later because it is involved in geometry so often!

Always remember: that every right triangle has at least one right angle.
There are two different types though:
30*,60*,90*
and
45*,45*,90*

Check out the visuals below. :)



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Triangles and Relationships that Appear Frequently and How to Use Them

Remember the Pythagorean Theorem?
A2 + B2 = C2

Yeah... That was a long time ago...

Here is more about the pythagorean theorem and triangles (things to remember from chapter 5).




Here are some common pythagorean triples:


Here are some more important notes involving the Pythagorean theorem and triangles. I could explain this in words if needed, but I figured that since I am strictly a visual learner, that this information in pictures will better help not only your understanding, but my understanding as well.




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Now we will move on to more information involving right triangles.

Triangle Division and Relationships

There are multiple types of triangles, but what is most important is to know what to remember about each type.

Here are some of the types:
Acute triangle - 3 acute angles
Equiangular Triangle - 3 congruent acute angles
Right Triangle - One right angle
Obtuse Triangle - One obtuse angle

Other things to note:
Equilateral Triangle - 3 congruent sides
Isosceles Triangle - at least 2 congruent sides
Scalene Triangle - No congruent sides

Other things to remember about triangles:
*NOTE, this symbol (<) is synonymous with angle
and this symbol (*) is synonymous with degrees
Triangle sum theorem: m
Acute angles of a right triangle are complementary.

The measure of each angle of an equiangular triangle is 60*

The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

If 2 angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent.


DON'T FORGET ABOUT
- SSS
- SAS
- ASA
- AAS
- HL
and CPCTC

THINGS TO NOTE:










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