Mark 2: 1-11

When Jesus healed the paralyzed man, all of his sins were forgiven. This shows us the amount of love that God has for us, and how we can be forgiven of our sins every day. This verse in very important, because it shows how even a paralyzed man with a lot of sins is still capable of God's love. If the four men that carried the man in through the roof decided not to go through all that trouble, the people would have not been able to see the amount of love and compassion God had for the sick people. Each and every day we are reminded of the love that God has for us, and how He sent His one and only son to die for us on the cross. God healed the man of his sins, before He healed his body. In this, He was showing how forgiving peoples sins was the highest priority over healing him physically.

Convex, Concave, and Regular Polygons

Convex: no line that contains a side of the polygon passes through the interior of the polygon

Concave: not convex

Regular: all sides and angles are congruent

Study Guide 7.4-7.6

7.4-

SSS Similarity Postulate- If the corresponding sides of two triangles are proportional, then, the two triangles are similar.

SAS Similarity Postulate- If an angle of one triangle is congruent to an angle of a second triangle and the length of the sides that include these angles are proportional, then the triangles are similar.

Symbols- If <x is congruent to <m and PM/ZX = MN/XY, then triangle XYZ is similar to triangle MNP

7.5- Proportions and Similar Triangles

Proportionality- 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

Symbols- In triangle QRS, if TU is parallel to RS, then RT/TQ = RU/US

Converse of the Triangle Proportionality Theorem- If a line divides two sides of a triangle proportionally, then it is parallel to the third side

Symbols- In triangle QRS, if RT/TQ = RU/US, then TU is parallel to QS

The Mid-segment Theorem- The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long

Symbols- In triangle ABC, if CD = DA, and CE = EB, then DE is parallel to AB and DE = 1/2 AB

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' so that P' lies on CP and CP' = 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 than the original, then the dilation is a reduction
If the image is LARGER than the original, then the dilation is an enlargement

Scale Factor-
The scale facts of a dilation is the ratio of CP' to CP. This ratio is also the scale factor of triangle P'Q'R' to triangle PQR.

Study Guide 7.1-7.3

7.1- Ratios and Proportions

Ratio- A ratio is a comparison of a number 2 and a nonzero number b using division.
Ratio 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, of the proportion. The numbers a and d are called e extremes of the proportion.

Cross Product Property~ In a proportion, the product of the extremes is equal to the produce of the means.

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 ice lengths are proportion;, then two polygons are similar.

Scale Factor- If two polygons are similar, then the ration of the side lengths of two polygons sides is called the scale factor.

Determining Similarity-
1) Check that corresponding angles are congruent
2) Check whether corresponding side lengths are proportional

Perimeters of Similar Polygons Theorem-
If two polygons are similar then the ratio of their perimeters is equal to the ratio of their corresponding side lengths

7.3- Angle- Angle Similarity

Angle- Angle Similarity Postulate- If two angles of one triangle are congruent to two angles of another triangle, then, the two triangles are similar

Symbols- If <k is congruent to <y and, <j is congruent to <x, then triangle jkl is similar to triangle xyz

The concept that challenged me the most was defiantly the similar polygons. I found it difficult to determine the discrepancies between the triangles, and to identify them as similar.

The concept that was the most rewarding to me was the ratios. I really liked to simplify ratios, and to dissect them all the way to the end.