4.2

According to Theorem 4.1 (Angle Sum)
The measures of the angles in a triangle are always equal to 180
m

If we know the measures of two angles, we can find the third measure.

if two angles of one triangle are congruent to two angles of another triangle, then the third angles of the triangles are not congruent.

Exterior Angle Theorem
The measure of one exterior is equal to the two interior angle measures added together.

A corollary is a statement that is easily proven with a theorem.
Corollary 4.1: acute angles of right triangles are always complimentary.
Corollary 4.2: there can only be one right angle or one obtuse angle in a triangle.

Section 3.5

Section 3.5 was about how you can prove that lines are parallel. You can prove that lines are parallel in many ways. One way is to use all of the converses that are in the dyno that we went over. They are corresponding, alternate exterior, and alternate interior converse. Also if the consecutive interior angles are supplementary then the line would be parallel. These are the ways to prove that lines are parallel.

Section 3-3 Review

This section covered slopes, slope formulas, slope relationships, slope-intercept form, and some review on parallel and perpendicular lines.

slope the ratio of a line's vertical rise to it's horizontal run

rate of change how much a quantity changes over time

The slope of parallel lines are always equal
The slope of perpendicular lines always are opposite reciprocals.
Skew Lines that are not coplanar and do not intersect at any point.

Slope-Intercept Form y=mx=b
point-slope form y-y1=m(x-x1)

Slopes Section 3.4

On October 13, we reviewed slopes.

Slope Intercept Form: y = m(x) + b
You must have the slope and the y-intercept.

Point Slope Form

y - y1 = m(x-x1)
You must have the slope and a point.

Section 3-2

In section 2-3 we learned about five different theorems and postulates for transversals



Alternative Interiorior and Exterior Theorums:
This states that so long as there are two parallel lines that are split by a transversal then the Alternate interior angles of those two parallel lines are congruent to each other. The same is true for Alternate exterior angles


Corresponding angles Postulate:
This one states that corresponding angles are congruent, so long as they are on two parrallel lines that are split by a transversal. At right is a picture showing two corresponding angles that are congruent.









Consecutive Interior Angles Theorem:
Consecutive Interior angles are supplementary so long as they are on two parellel lines that are split by a transversal. This means that the sum of both he consecutive interior angles is 180 degrees. To the right is an example.




Perpendicular transversal theorem:
States that if a transversal is perpendicular to one of two parallel lines then it is perpendicular to the other one. example shown below

October 8, 2008

In class today we learned about lines and transversal. There are three kinds of lines, parallel lines, skew lines and parallel planes. Parallel lines are 2 lines that are coplanar but don't intersect. Skew Lines are 2 lines that are not coplanar and do not intersect. Parallel planes are 2 planes that do not intersect. We also talked about about transversal. Transversal is a line that intersect two or more non coplanar lines and creates angles. There are 4 types, corresponding angles, alternate exterior, alternate interior, consecutive interior. Corresponding angles are angles that correspond from each other, nonadjacent, same side of the trensversal, and one exterior while one is interior. Alternate exterior angles are exterior angles that lie on either side of the rensversal making a linear pair. Alternate Interior angles lie inbetween the non coplanar lines, lie on either side of the transversal, and are non adjacent. Consecutive Interior angles are angles that lie on the same side of the transversal on the interior.

Examples

Parallel Lines

Skew Lines

Parallel Planes

Corresponding angles

Alternate Exterior

Alternate Interior

Consecutive Interior

Section 2.6 Reasoning With Algebra

This is what we learned in the 2.6 chapter. These are the Dyknow slides. We learned about the properties, and it was the beginning of learning about the proofs.

2.6