Tyler

> Can I have 2 sides and an angle?
>
> Tyler, Geometry Unit 2, Lesson 4.3

**Tyler** is likely the nicest one of the Illustrative Mathematics characters. He is social, and very giving. His tendencies include sharing paper with peers. Tyler is also a very hard worker, especially when it comes to math. Unfortunately for him, he is consistently incorrect. It is implied that he likes the subject of science.

Tyler's only friends are Jada and Priya. Specifically, he may have a crush on Priya, although she is in a relationship with Han and he would never break that.

Tyler's favorite subject is science.

## Notable Appearances

**Geometry Unit 1**

* "Tyler thinks angle EBF is congruent to angle BCD because they are corresponding angles and a translation along the directed line segment from B to C would take one angle onto the other." (Lesson 21.1)

*Analysis: This, along with the list of reasons Tyler wrote afterwards to support his theory, supports the theory that he puts more effort into his math than most. Still, he is incorrect.*

**Geometry Unit 3**

* "Tyler wrote a proof that all rectangles are similar." (Lesson 8.2)

*Analysis: The extremely long proof that Tyler writes following this supports the theory that Tyler puts more effort into math than most others. Still, he is incorrect here.*

**Geometry Unit 5**

* "Tyler is designing a banner that will welcome people to a festival." (Lesson 6, Practice Problems)

*Analysis: This shows how kind of a person Tyler is, as well as how hard he works.*

**Geometry Unit 7**

* "Han and Tyler are each completing the same set of tasks on an online homework site. Han is using his smartphone and Tyler is using his tablet computer. Their progress is indicated by the circular bars shown in the image. The shaded arc represents the tasks that have been completed. When the full circumference of the circle is shaded, they will be finished with all the tasks. Tyler says, 'The arc length on my progress bar measures 4.75 centimeters. The arc length on Han’s progress bar measures 2.25 centimeters. So, I’ve completed more tasks than Han has.'" (Lesson 10.1)

*Analysis: In this problem, Tyler is not considering size of screen at all. This supports the theory that, despite how hard he tries, he is not very smart at all.*

**Algebra 2 Unit 1**

* "Tyler has a piece of paper and is sharing it with Elena, Clare, and Andre. He cuts the paper to create four equal pieces, the hands one each to the others and keeps one for himself." (Lesson 11.2)

*Analysis: This shows how truly kind and giving Tyler is to others.*

**Algebra 2 Unit 5**

* "Tyler leaves his house at 7:00 a.m. to go to school. He walks for 20 minutes until he reaches his school, 1 mile from his house. (Lesson 3, Practice Problems)

*Analysis: Confirms not only Tyler's morning schedule and the distance between his house and his school, but also confirms Tyler's walking speed.*

* "On snowy days, Tyler's school has a 2 hour delayed start time (120 minutes)." (Lesson 3, Practice Problems)

*Analysis: Confirms that the Illustrative Mathematics students must go to school in a part of the world where it snows.*

**Algebra 2 Unit 7**

* "Tyler is interested in how different environments affect dandelion plants. For a science fair project, Tyler looks for dandelions growing the grass and growing in dirt without grass. He counts the number of days it takes each dandelion to turn from a yellow flower into seeds." (Lesson 2, Practice Problems)

*Analysis: This implies that Tyler likes science.*

* "Han and Priya are studying the sizes of trees next to their school. They each take a random sample to find the proportion of trees that have a trunk circumference greater than 4 feet. Tyler's sample contains 12 trees, and Priya's sample contains 20 trees. After collecting data, they run 100 simulations each to determine an estimate for the proportion of trees with large trunk circumferences." (Lesson 11, Practice Problems)

*Analysis: Uhhhh I don't know what this means tbh. Han and Tyler switch halfway through the problem???*

## Miscellaneous Appearances

**Geometry Unit 1**

* "Kiran thinks both diagonals of a kite are lines of symmetry. Tyler thinks only one diagonal is a line of symmetry." (Lesson 15.3)

**Geometry Unit 2**

* "Tyler says that ASDPX is congruent to SMDZH because sides AS and MS are corresponding." (Lesson 3, Practice Problems)
* "Tyler has written an incorrect proof to show that quadrilateral ABCD is a parallelogram." (Lesson 6, Practice Problems)
* "Tyler has proven that triangle WYZ is congruent to triangle WYX using the Side-Side-Side Triangle Theorem." (Lesson 10, Practice Problems)

**Geometry Unit 5**

* "Tyler and Jada wish to find the value of x, the length of side BC in this triangle. Tyler decides to set up the equation tan(56) = 8/x. Jada says she prefers an equation that has x in the numerator." (Lesson 4, Practice Problems)

**Geometry Unit 7**

* "Tyler and Kiran are discussing the parallelogram in the image. Tyler says the parallelogram cannot be cyclic. Kiran says the parallelogram can be cyclic if a circle is drawn carefully through the vertices." (Lesson 6, Practice Problems)
* "Tyler is confident that all circles are similar, but he cannot explain why this is true." (Lesson 10, Practice Problems)

**Algebra 2 Unit 2**

* "Tyler finds an expression for V(x) that gives the volume of an open-top box in cubic inches in terms of length x in inches of the square cutouts used to make it." (Lesson 2, Practice Problems)
* "Jada and Tyler were playing the Info Gap, using Card 3. Tyler asked, 'Can I have 2 sides and an angle?' Jada told Tyler that one angle was 16, one side was 5 cm, and one side was 4 cm." (Lesson 4.3)
* "Tyler incorrectly says that the constant term of (x + 4)(x - 4) is zero." (Lesson 6, Practice Problems)
* "Tyler thinks he knows one of the linear factors of P(x) = x^3 - 9x^3 + 23x - 15. After finding that P(1) = 0, he suspects that x - 1 is a factor of P(x)." (Lesson 12, Practice Problems)

**Algebra 2 Unit 3**

* "Tyler was solving this equation: x^2 - 1 = 3. He said, 'I can add 1 to each side of the equation and it doesn't change the equation. I get x^2 = 4. Priya said, "It does change the equation. It just doesn't change the solutions!' Then she showed these two graphs. Tyler said, 'Now I can take the square root of each side to get the solution to x^2 = 4. The square root of x^2 is x. The square root of 4 is 2.' He wrote: x^2 = 4, √x^2 = √4, x = 2. Priya said, 'But now the graphs show that there are *two* solutions!'" (Lesson 7.2)
* "Here are the steps Tyler took to solve the equation √(x +3) = -5." (Lesson 9, Practice Problems)

**Algebra 2 Unit 4**

* "Tyler says the sequence 1, 1, 1,... of repeating 1s is not exponential because it does not change." (Lesson 1, Practice Problems)
* "Tyler says that the function f(x) = 5^x is exponential so it grows by equal factors over equal intervals." (Lesson 7, Practice Problems)
* "To solve the equation 10^m = 19, Tyler writes the equation in the logarithmic form: m = log10(19). He then presses the "log" button on the calculator, enters the number "19", and writes down an approximation of 1.279. Priya follows the same steps on her calculator and writes down 1.27875." (Lesson 11.3)
* "Using the fact that 2^10 = 1024, Tyler estimates that 2^20 is about 1,000,000, and log2(1,000,000) is about 20." (Lesson 18, Practice Problems)

**Algebra 2 Unit 7**

* "Tyler looks at this histogram of a distribution with a mean of 6.7 grams and a standard deviation of 1 gram." (Lesson 7, Practice Problems)