# Second Semester Geometry

## Chapter 6: Similar Figures

Big Ideas
1. 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.
2. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
3. Similar figures are shapes that have the same shape and angles but different sizes.
4. If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.
5. If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
6. 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.
7. The segment connecting the midpoints of two sides of a triangle is paralles to the third side and is half as long.
8. If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

## Tips!

1. 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.
2. Understand how to cross multiply because it makes finding if things are similar much easier.
3. 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.
4. If a side is larger the angle opposite of it must open up wider in order to fit the line in.
5. 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.
6. Corresponding angles of congruent figures should be equal.

## What I Struggled With

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

## Vocabulary

1. Triangle- A shape with three sides that are not curved and all sides are closed.
2. Congruent- Being the same shape and having the same size angles but not necessarily being the same size.
3. Similar Polygons- Polygons with te same shape but different sizes.
4. SSS- Side side side
5. SAS- Side angle side
6. AA- Angle angle
7. Midsegment- Segment that connects tow midpoints of a triangle.
The text passage is a summary of key concepts, tips, and vocabulary from a chapter on similar figures in a geometry textbook. It does not contain any specific mathematical questions or answers.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Second Semester Geometry

## Chapter 6: Similar Figures

Big Ideas
1. 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.
2. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
3. Similar figures are shapes that have the same shape and angles but different sizes.
4. If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.
5. If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
6. 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.
7. The segment connecting the midpoints of two sides of a triangle is paralles to the third side and is half as long.
8. If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

## Tips!

1. 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.
2. Understand how to cross multiply because it makes finding if things are similar much easier.
3. 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.
4. If a side is larger the angle opposite of it must open up wider in order to fit the line in.
5. 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.
6. Corresponding angles of congruent figures should be equal.

## What I Struggled With

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

## Vocabulary

1. Triangle- A shape with three sides that are not curved and all sides are closed.
2. Congruent- Being the same shape and having the same size angles but not necessarily being the same size.
3. Similar Polygons- Polygons with te same shape but different sizes.
4. SSS- Side side side
5. SAS- Side angle side
6. AA- Angle angle
7. Midsegment- Segment that connects tow midpoints of a triangle.
user
The text passage is a summary of key concepts, tips, and vocabulary from a chapter on similar figures in a geometry textbook. It does not contain any specific mathematical questions or answers.

TYPE: NO_QUESTION