Han

> Really? We know if the lines are parallel then the alternate interior angles are congruent, but I didn't know that it works both ways.
>
> Han, Geometry Unit 1, Lesson 20 Practice Problems

**Han** is in a relationship with Priya, which is the only relationship between Illustrative Mathematics characters that does not involve an affair with Andre in some way or another. Han is also friends with Clare and Elena.

The only thing that is important to note about Han is that he is bad with technology and math. He may also be a bridge enthusiast.

## Notable Appearances

**Geometry Unit 1**

* "Han thought he constructed a rectangle using digital tools. When he moved point A the screen looked like this." (Lesson 8, Practice Problems)

*Analysis: The fact that Han messed up his rectangle due to lack of knowledge regarding digital tools shows that he is bad with technology.*

* "Priya: 'I bet if the alternate interior angles are congruent, the lines will have to be parallel.' Han: 'Really? We know if the lines are parallel then the alternate interior angles are congruent, but I didn't know that it works both ways.' Priya: 'Well, I think so. What if angle ABC and BCJ are both 40 degrees? If I draw a line perpendicular to line AI through point B, I get this triangle. Angle CBX would be 50 degrees be 40 + 50 = 90. And because the angles of a triangle sum to 180 degrees, angle CXB is 90 degrees. It's also a right angle!' Han: 'Oh! Then line AI and line GJ are both perpendicular to the same line. That's how we constructed parallel lines, by making them both perpendicular to the same line. So lines AI and GJ must be parallel.'" (Lesson 20, Practice Problems)

*Analysis: Not only do Priya and Han often appear together, this example specifically shows that they may have a deeper connection, considering how much fun they're having, which definitely can't be because of the math itself.*

**Geometry Unit 2**

* "Han and Priya were making a kite. Han cut out a piece of fabric so that there were 2 short sides of the same length on top and 2 long sides of the same length on the bottom. Priya cut 2 pieces of wood to go across the diagonals of the kite. They attached the wood like this: Han asked Priya to measure the angle to make sure the pieces of wood were perpendicular. Priya said, 'If we were careful about the lengths of the sides of the fabric, we don't need to measure the angle. It has to be a right angle.'" (Lesson 8, Practice Problems)

*Analysis: The fact that Priya and Han are making a kite together shows that they may be in a relationship.*

* "Han, Clare, and Andre thought of a way to construct an angle bisector. They used a circle to construct points D and E the same distance from A. Then they connected D and E and found the midpoint of segment DE. They thought that ray AF would be the bisector of angle DAE." "Han's rough-draft justification: F is the midpoint of segment DE. I notices that F is also on the perpendicular bisector of angle DAE." (Lesson 14.2)

*Analysis: Han's appearance with Andre may imply that they are friends.*

**Geometry Unit 4**

* "Priya says, 'I know everything about a right triangle with a 30 degree angle and a hypotenuse of 1 cm. Here, look.' Han asks, 'What would happen if a triangle with a 30 degree angle has a hypotenuse that is 2 cm instead?'" (Lesson 4, Practice Problems)

*Analysis: This appearance with Priya and Han supports the theory that they are in a relationship.*

**Geometry Unit 6**

* "Priya and Han each wrote an equation of a line with slope 1/3 that passes through the point (1,2). Priya’s equation is y - 2 = 1/3(x - 1) and Han’s equation is 3y - x = 5." (Lesson 10, Practice Problems)

*Analysis: This appearance supports the theory that Priya and Han are dating.*

**Algebra 2 Unit 5**

* "Han wants to model the shape of the arch with the graph of a function, and he chooses H(x) = x(52 - x), where H(x) is the height in meters above a point x meters along the base of the arch from the left end." (Lesson 8.2)

*Analysis: Han may be a bridge enthusiast.*

**Algebra 2 Unit 7**

* "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 2**

* "Elena wonders whether she could play the Info Gap with area included as an extra piece of information from the data card. She draws a card with this information and asks Han to play." (Lesson 4.2)
* "Han wrote a proof that triangle BCD is congruent to triangle DAB. Han's proof is incomplete." (Lesson 7, Practice Problems)

**Geometry Unit 3**

* "Han then states that the 2 triangles created by diagonal EG must be congruent." (Lesson 5, Practice Problems)

**Geometry Unit 4**

* "Clare and Han are discussing how to find the missing lengths. Clare says she is using similarity. Han says he is using Pythagorean Theorem." (Lesson 2, Practice Problems)

**Geometry Unit 7**

* "Jada cuts out a rectangular piece of paper that measures 5 inches by 4 inches. Han cuts out a paper sector of a circle with radius 5 inches, and calculates the arc length to be 2pi inches." (Lesson 9, Practice Problems)
* "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)
* "Han thinks that since the arc length in circle A is longer, its central angle is larger." (Lesson 11, Practice Problems)

**Algebra 2 Unit 2**

* "Han notices: 11^2 = 121 and (x + 1)^2 = x^2 + 2x + 1, 11^3 = 1331 while (x + 1)^3 = x^3 + 3x + 1" (Lesson 2.2)
* "Han is multiplying 10x^4 and 0.5x^3 and gets 5x^7. He says that 0.5x^3 is not a polynomial because 0.5 is not an integer." (Lesson 5, Practice Problems)
* "Han was solving this equation: (x + 3)/2 = 4. He said, 'I know that half of x +3 = 4. So x + 3 must be 8, since half of 8 is 4. This means that x is 5.'" (Lesson 7.3)\

**Algebra 2 Unit 3**

* "Elena and Han solved the equation x^2 - 6x + 7 = 0 in different ways." (Lesson 16.2)

**Algebra 2 Unit 5**

* "Elena thinks that shifting up the graph of f up by 50 will match the data. Han thinks that shifting the graph of f up by 60 and then right by 1 will match the data." (Lesson 3, Practice Problems)