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.
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