Mark 2:1-11

   In the book of Mark, Jesus comes to Capernaum to preach. The streets flooded with people so not everyone could fit in the building he preached in. Four men brought a paralyzed man to see Jesus, but they could not reach him due to the large numbers of people. The men lowered the cripple through the roof of the building Jesus was in. Jesus god the man that he had been forgiven for his sins, and commanded the man to walk out of the room, and so, he walked. 

   Something that stood out to me the most was the fact that before allowing the paralyzed man to walk, he forgave him of his sins. What the people didn't understand was the fact that sins were more crippling than a disability. Jesus freed the man from being paralyzed, but he also freed him from his sins which is more important. 

7.4 - 7.6

7.4: SSS and SAS Similarity

SSS Similarity Postulate:

   If the corresponding sides of two triangles are proportionate, then the two triangles are similar.

SAS Similarity Postulate:

   If an angle of one triangle and the length of the sides that include these angles are proportionate, then the triangles are similar.

Nothing was difficult in this section

7.5: Proportions and Similar Triangles

Proportionality:

   If GP:PH = JQ:QK then GH and JK are divided proportionally 

Triangle Proportionality Theorem:

   If a line parallel to one side of a triangle intersects 

the other sides, then it divides the two sides proportionally.

Converse of the Triangle Proportionality Theorem:

   If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

Midsegment Theorem:

   The segment connecting the midpoints of two sides of a triangle is

parallel to the third side and it is half as long.

Nothing in this section challenged me

7.6: Dilations

Dilation: 

   A dilation is a transformation with center C and scale factor K that maps each point P to an image point P(prime) so that P(prime) lies on CP and CP(prime) = K x CP.

   A dilation maps a figure onto a similar figure called the image.

   In a dilation, every image is similar to the original figure.

Types of Dilations:

   If the image is smaller then the original, the dilation is a reduction.

   If the image is larger than the original, the dilation is an enlargement.

Scale Factor:

   The scale factor of a dilation is the ratio of CP(prime) to CP.

   

The most challenging thing in this section was the scale factor. I learned that, once I found that CP(prime) is always over CP, the scale factor wasn't hard to figure out.

Overall:

   Overall, I thought the most challenging thing was the scale factor and how to find it. I eventually figured out that CP(prime) is over CP and from there, I could find the ratio of the scale factor. 

Chapters 7.1 - 7.3

7.1: Ratios and Proportions

A ratio is a comparison of a number a and a nonzero number b using division.

    Ratios can be written in four different ways.

    Ratios are usually written in simplest form.

An equation that states two ratios are equal is called a proportion 

    In the proportion A:B = C:D, the numbers B and C are called the means, and A and D are the extremes 

In a proportion, the product of the extremes is equal to the product of the means

In this lesson, the means and extremes were the things to trip me up the most. I learned to just remember that, when set up in factor form, the means were always the bottom number of the first listed ratio and its diagonal, and the extreme was the top number of the first ratio and its diagonal.

7.2: Similar Polygons

Similarity:

Two figures that have the same shape, but not necessarily the same size are called similar

Similar Polygons:

If corresponding angles are congruent and corresponding side lengths are proportional, then the two polygons are similar polygons.

Scale Factor:

If two polygons are similar, then the ratio of the lengths of two corresponding sides is called the scale factor

Determining Similarity:

   1 Check that corresponding angles are congruent

   2 Check whether the corresponding side lengths are proportional

Perimeters of Similar Polygons Theorem:

If two polygons are similar then the ratio of their perimeters is equal to their corresponding side length

This lesson was easy for me, and I didn't really have any problems.

7.3 Angle-Angle Similarity

Angle-Angle Similarity Postulate:

If 2 angles of one triangle are congruent to 2 angles of another triangle, then the two triangles are similar

In the lesson, the angle-angle similarity was easy and I didn't really have any issues with it.

Overall, the lessons were fairly easy and the most challenging things were the means and extremes. As the lessons went on, I learned how to differentiate between the tow of them and I don't have any concerns for these lessons going forward.