This section used proportions to find the lengths of sides with the known information. Utilizing this is simple and easy. If you have one variable you can figure it out by using your proportions. We know that in all triangles (or "parts" of ones) with a parallel line in inside of the triangle, the two sides that are split in two are proportional. Knowing this information can help with proofs and other problems.

7.2

Today, we learned about how you find if polygons are similar or not.  In this slide, it shows how to represent similarity between two pieces of polygons with the squigly symbol.  

Also, if you know polygons are similar, you now know that all of the angles in that polygon are congruent. 

 

Section 6.6-Trapazoids and Kites

Today we learned about trapezoids and kites. Some of the characteristics of a trapezoid are that it has two parallel lines and those lines are the bases. Also the non-parallel sides are the legs. The kites have two congruent angles and these angles are the angles from the non congruent sides. The kites are only quadrilaterals and do not belong to the parallelogram family and the trapezoids do. That is what we learned from section 6.6 and the DyKnow above helps explain the kites and trapezoids more thoroughly.

6.4

A rectangle is just another parallelogram but the difference is that a rectangle has 4 right angles. Also a parallelogram is considered a rectangle if its diagnols are congruent with each other. By using the Rectangle diagnol theorem we can prove that a parallelogram is a rectangle

Section 6-1

Today we learned how to find the measure of each individual angle of regular polygons with different numbers of sides. (n-2) * 180 is the formula that we use to do that. The N is represnting how many triangles are found in the regular convex polygon we are trying to find the measures of the angles of. Then when using that formula and simplifying it you divide the whole problem by N again representing each individual angle.

(N-2) * 180

_________

       N

                

We also learned how to find the measure of each exterior angle. All the exterior angles added together make the sum of 360. Then all you have to do is divide by N to get each individual angle.

       

     360

_______

       N

section 6-3 parallelograms

Proving quadrilaterals are parallelograms.
One opposite pair of sides theorem: if one pair of sides of a quadrilateral are parallel and congruent, then it is a parallelogram.

More ways to prove a quadrilateral is a parallelogram:
Both pairs of opposite sides are parallel
both pairs of opposite sides are congruent
both pairs of opposite angles are congruent
any angle is supplementary to both of its consecutive angles
diagonals bisect eachother
one pair of opposite sides are congruent and parallel

We learned today how to find the sum of all of the interior angles in a convex polygon and how to find the sum of each interior angle. It is called the Interior angles theorem. (n stands for number of sides)

We also found out that all exterior angles of a polygon will add up to 360 no matter what. To find the measure of each exterior angle just divide 360 by n.

Section 6.2: Parallelograms

hToday in class we learned about parallelograms. We learned:

· The diagonals in a polygon are segments joining two nonconsecutive sides

# of diagonals in a polygon = the number of sides minus 2.

· A parallelogram is a quadrilateral with both pairs of opposite sides that are parallel

Opposite Sides Theorem:

The opposite sides of a parallelogram are congruent

Opposite Angles Theorem:

The opposite angles of a parallelogram are congruent

If one angle is 90 degrees, then all four angles are 90 degrees

Consecutive Angles Theorem:

Consecutive angles in a parallelogram are supplementary

Ex: the measure of angle S is congruent to the measure of angle A

The measure of angle A is congruent to the measure of angle T

The measure of angle N is congruent to the measure of angle S

The measure of angle T is congruent to the measure of angle N

Parallel Diagonal Theorem:

In a parallelogram, the diagonals will bisect each other

Section 5.4.

Shortest Distance Theorem- the perpendicular segment from a point to a line is the shortest segment from the point to the line.

Triangle Inequality Theorem- the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Corollary 5.1- The perpendicular segment from apoint to a plane is the shortest segment from the point to the plane.

Sec 5.5

Hinge Theorem (SAS Inequality)
-If two sides of one triangle are congruent to two sides of another triangle and the included angle of the 1st is larger than the included angle of the 2nd, then the 3rd side of the 1st is longer than the 3rd side of the 2nd.

Converse of Hinge Theorem (SSS Inequality)
-If two sides of one triangle are congruent to two sides of another triangle and the third side of the first is longer than the third side of the 2nd, then the included angle of the 1st is larger than the included angle of the 2nd.