# Second Semester Geometry

### Survival Guide

## Chapter 6: Similar Figures

Big Ideas

- If one side of a triangle is longer than another side of a triangle then the angle opposite of the larger side will be bigger than the angle opposite the smaller side.
- The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
- Similar figures are shapes that have the same shape and angles but different sizes.
- If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.
- If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
- If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.
- The segment connecting the midpoints of two sides of a triangle is paralles to the third side and is half as long.
- If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

## Tips!

- When trying to see of three sides will make a triangle just remember to add the smaller two sides together and if they are bigger than the biggest side then you can make a triangle.
- Understand how to cross multiply because it makes finding if things are similar much easier.
- Remember that just because the side lengths of a shape double doesn't mean that the angles double. The angles would stay the same size.
- If a side is larger the angle opposite of it must open up wider in order to fit the line in.
- When dilating a figure it should look the same just smaller. If you divide one side by two you have to divide all sides by two.
- Corresponding angles of congruent figures should be equal.

## What I Struggled With

## What I Struggled With

- I struggled with setting up cross multiplication. Sometimes I put numbers in the wrong place.
- Sometimes if i divided a side by two i also divided an angle by two.
- When I would make some of my dilated shapes the smaller shape would not be congruent.
- Finding corresponding sides in shapes was hard sometimes.
- Remembering SSS, SAS, and AA was hard for me to do.
- At first I couldn't find mid segments at all.

## Vocabulary

- Triangle- A shape with three sides that are not curved and all sides are closed.
- Congruent- Being the same shape and having the same size angles but not necessarily being the same size.
- Similar Polygons- Polygons with te same shape but different sizes.
- SSS- Side side side
- SAS- Side angle side
- AA- Angle angle
- Midsegment- Segment that connects tow midpoints of a triangle.