Lin

> I thought that too at first, but now I think that a parallelogram does have rotation symmetry. Here, look at this.
>
> Lin, Geometry Unit 1, Lesson 16.3

**Lin** is probably the most athletic of the characters. She plays handball, golf, and basketball. It is also important to note that she is having an affair with Andre, and perhaps she wants him all to herself, because she is likely quite angry about something, given that she frequently disagrees with others in math class. Lin's only other friend is Diego.

## Notable Appearances

**Geometry Unit 1**

* "Clare says, 'Last class I thought the parallelogram would have reflection symmetry. I tried using a diagonal as the line of symmetry but it didn't work. So now I'm doubting that it has rotation symmetry.' Lin says, "I thought that too at first, but now I think that a parallelogram does have rotation symmetry. Here, look at this.'" (Lesson 16.3)

*Analysis: This is an example of Lin going out of her way to disagree with someone. This furthers the theory that she is angry about something.*

**Geometry Unit 2**

* "Lin thinks thinks these triangles must be congruent. Priya says she knows they might not be congruent." (Lesson 11, Practice Problems)

*Analysis: In this instance, although Lin does not instigate the disagreement, she does participate in one. This furthers the theory that she is angry about something.*

**Geometry Unit 3**

* "Lin is trying to convince Andre that all circles are similar." (Lesson 9, Practice Problems)

*Analysis: This is an example of Lin going out of her way to disagree with someone. This furthers the theory that she is angry about something.*

* "Lin is playing hand ball and wants the ball to bounce off wall CB and land at D." (Lesson 16, Practice Problems)

*Analysis: This confirms that Lin plays hand ball.*

**Geometry Unit 5**

* "A triangle has area 100 square inches. It's dilated by a factor of k = 0.25. Mai says, 'The dilated triangle's area is 25 square inches.' Lin says, 'The dilated triangle's area is 6.25 square inches.'" (Lesson 5.2)

*Analysis: This is an example of Lin going out of her way to disagree with someone. This furthers the theory that she is angry about something.*

* "Mai, Andre, and Lin are discussing the volume of a scaled box. The original holds 7 cubic inches. The new box holds 448 cubic inches. Mai thinks the scale factor is 4, Andre thinks the scale factor is 16, and Lin thinks the scale factor is 64." (Lesson 14, Practice Problems)

*Analysis: This is an example of Lin going out of her way to disagree with someone. This furthers the theory that she is angry about something.*

**Algebra 2 Unit 1**

* "Andre and Lin are asked to write an equation for S that isn't recursive." (Lesson 8.3)

*Analysis: This is an example of Lin appearing with Andre, which happens multiple times, furthering the theory that they are in a relationship.*

**Algebra 2 Unit 4**

* "Lin is saving $300 per year in an account that pays 4.5% interest per year, compounded annually." (Lesson 4, Practice Problems)

*Analysis: This confirms that Lin is good with money.*

**Algebra 2 Unit 7**

* "When Lin drives a golf ball, it travels a mean distance of 200 yards with a standard deviation of 20 yards, and the distribution of lengths is approximately normal." (Lesson 7, Practice Problems)

*Analysis: Lin plays golf.*

* "Lin, Kiran, and Diego are going to shoot 100 free throws each for practice. Based on their shooting in the past, Lin thinks they are all of similar ability, and Lin estimates that they each have a 60% chance of making each shot. They each shoot their shots. Lin makes 63 of the 100 shots. Kiran makes 75 of the 100 shots. Diego makes 35 of the 100 shots." (Lesson 8.1)

*Analysis: Lin plays basketball, and she is decent at it.*

## Miscellaneous Appearances

**Geometry Unit 2**

* "Triangle ABC is congruent to triangle EDF. So, Lin knows that there is a sequence of rigid motions that takes ABC to EDF." (Lesson 5, Practice Problems)
* "Lin is using the diagram to prove the statement, 'If a parallelogram has one right angle, it is a rectangle.'" (Lesson 12, Practice Problems)

**Geometry Unit 3**

* "Lin is using the diagram to prove the statement, 'If a parallelogram has one right angle, it is a rectangle.'" (Lesson 5, Practice Problems)

**Geometry Unit 4**

* "Lin says she has memorized the lengths of a few right triangles, for example, 3, 4, and 5. She is trying to compile a list of several right triangles." (Lesson 1, Practice Problems)

**Geometry Unit 7**

* Lin is looking at cyclic quadrilateral ABCD. She says, 'I’m not convinced that opposite angles of cyclic quadrilaterals always add up to 180 degrees. For example, in this diagram, suppose we moved point A to a different spot on the circle. Angle BCD would still measure 100 degrees, but now angle BAD would have a different measure, and they wouldn’t add up to 180.'" (Lesson 4, Practice Problems)
* "Diego and Lin are looking at 2 circles. Diego says, 'It seems like for a given central angle, the arc length is proportional to the radius. That is, the ratio l/r has the same value as the ratio L/R because they have the same central angle measure. Can we prove that this is true?' Lin says, 'The big circle is a dilation of the small circle. If k is the scale factor, then R = kr.' Diego says, 'The arc length in the small circle is l = 0/360 x 2pir. In the large circle, it’s L = 0/360 x 2piR. We can rewrite that as L = 0/360 x 2pirk. So L = kl.' Lin says, 'Okay, from here I can show that l/r and L/R are equivalent.'” (Lesson 11.2)
* "Lin thinks that the central angle in circle A is congruent to the central angle in circle B." (Lesson 12, Practice Problems)
* "Lin and Elena are trying to find the area of the shaded sector in the image. Lin says, 'We’ve found sector areas when the central angle is given in degrees, but here it’s in radians. Should I start by finding the area of the full circle?' Elena says, 'I saw someone using the formula 1/2r^2 0 where 0 is the measure of the angle in radians, and r is the radius. But I don’t know where that came from.'” (Lesson 13.2)

**Algebra 2 Unit 2**

* "Lin divides the polynomial 2x^2 - 4x + 1 by 4 and gets 0.5x^2 - x + 0.25." (Lesson 4, Practice Problems)

**Algebra 2 Unit 3**

* "Lin says, 'When you add or multiply two complex numbers, you will always get an answer you can write in a + bi form.' Noah says, 'I don't think so. Here are some exceptions I found.'" (Lesson 13, Practice Problems)

**Algebra 2 Unit 6**

* "Lin calculates 0.97^2 + 0.26^2 and finds that it is 1.0085." (Lesson 4, Practice Problems)

**Algebra 2 Unit 7**

* "Lin is working on a science experiment. She wants to determine whether salt water boils faster than freshwater." (Lesson 12, Practice Problems)