Priya

> Well, I think so. What if angle ABC and BCJ are both 40 degrees?
>
> Priya, Geometry Unit 1, Lesson 20 Practice Problems

**Priya** is in a relationship with Han, which is the only relationship between Illustrative Mathematics characters that does not involve affairs in some way or another.

Other interesting things to note about Priya are that she is friends with Noah, who she likes to play Invisible Triangles and ride Ferris wheels with, that she has a younger cousin whom she adores, and that she enjoys walking down hallways in very unusual ways. She also likes playing handball, which she most likely does with Lin. She is also friends with Tyler.

Priya may be going through times of financial hardship, being forced to borrow money from her grandmother. Alternatively, this could be to buy a present for Han.

## Notable Appearances

**Geometry Unit 1**

* "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**

* "Noah and Priya were playing Invisible Triangles." (Lesson 3.3)

*Analysis: Priya and Noah may be friends, who seem to enjoy playing Invisible Triangles together.*

* "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.*

**Geometry Unit 4**

* "Priya is teaching her younger cousin to ride a bike. She wants to stay on roads that are not too steep and easy enough for a new bike rider. She has decided the roads must have an angle less than or equal to 7 degrees." (Lesson 2, Practice Problems)

*Analysis: Not only does Priya seem to like her younger cousin, she seems very protective and genuinely concerned about their health.*

* "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.*

* "Priya is playing hand ball and wants the ball to bounce off wall CB and land at D." (Lesson 8, Practice Problems)

*Analysis: This confirms that Priya plays handball. Given that Lin also plays handball, it is likely that the two of them play together.*

**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.*

**Geometry Unit 7**

* "Priya and Noah are riding different size Ferris wheels at a carnival. They started at the same time."

*Analysis: This confirms that Priya likes Ferris wheels. It also supports the theory that she is friends with Noah.*

**Algebra 2 Unit 1**

* "Priya is walking down a long hallway. She walks halfway and stops. Then, she walks half of the remaining distance, and stops again. She continues to stop every time she goes half of the remaining distance." (Lesson 11, Practice Problems)

*Analysis: This shows that Priya likes to walk down hallways in really strange ways?*

**Algebra 2 Unit 4**

* "Priya borrowed $160 from her grandmother. Each month, she pays off one fourth of the remaining balance that she owes." (Lesson 2,1)

*Analysis: Not only does this confirm that Priya has a grandmother, but she must also be facing financial hardship if she has to borrow money from her.*

**Algebra 2 Unit 7**

* "Pryia flips her coin 20 times and it lands showing heads twice." (Lesson 8.2)

*Analysis: Although we cannot confirm it, Priya may be using an unfair coin. If she can't even be fair and trustworthy at flipping coins, how can we trust her about anything at all? Just some thoughts.*

* "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**

* "Diego observes that although it was often easier to use a sequence of reflections, rotations, and translations to describe the rigid transformations in the cards, each of them could be done with just a single reflection, rotation, or translation. However, Priya draws on her card, shows, which she claims can not be done as a single reflection, rotation, or translation." (Lesson 17.2)

**Geometry Unit 2**

* "Triangle ABC is congruent to triangle EDF. So, Priya knows that there is a sequence of rigid motions that takes ABC to EDF." (Lesson 6, Practice Problems)
* "Priya was given this task to complete:" (Lesson 9.2)
* "Lin thinks these triangles must be congruent. Priya says she knows they might not be congruent." (Lesson 11, Practice Problems)
* "Priya makes a claim that triangle AEB is congruent to triangle DBE." (Lesson 14, Practice Problems)
* "Priya is convinced the diagonals of the isosceles trapezoid are congruent. She knows that if she can prove triangles congruent that include the diagonals, then she will show that diagonals are also congruent." (Lesson 14, Practice Problems)

**Geometry Unit 3**

* "Priya is trying to determine if triangle ADC is congruent to triangle CBA. She knows that segments AB and DC are congruent. She also knows that angles DCA and BAC are congruent." (Lesson 14, Practice Problems)

**Geometry Unit 6**

* "Priya writes a proof saying: Consider any 2 parallel lines. Assume they are not horizontal or vertical. Therefore they must pass through the x-axis as well as the y-axis. This forms 2 right triangles with a second congruent angle. Call the angle x. The tangent of x is equal for both triangles. Therefore the lines have the same slope." (Lesson 10.2)

**Geometry Unit 7**

* "Kiran says, 'We can find the area of the whole circle, the arc length of the sector, and the circumference of the circle with this information.' Priya says, 'But how? We don’t know the circle’s radius!'" (Lesson 9.2)
* "Priya and Mai are trying to prove that if 2 chords are congruent, they are equidistant from the center of the circle. Priya draws this picture. Mai adds the perpendicular segment from the center of the circle to each chord. Priya says, 'I think we should try to use triangles because that is how we proved things congruent before.' Mai says, 'I think you’re right, but how? Should we draw in some radii?'" (Lesson 9, Practice Problems)

**Algebra 2 Unit 2**

* "Priya wants to sketch a graph of the polynomial f defined by f(x) = x^3 + 5x^2 + 2x - 8." (Lesson 12.2)

**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)
* "Priya is using the quadratic formula to solve two different quadratic equations." (Lesson 18, Practice Problems)

**Algebra 2 Unit 4**

* "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)

**Algebra 2 Unit 5**

* "Priya is thinking about the windmill in an earlier lesson. That windmill had a point P at (1, 0) at the end of the blade that starts at 0 radians pointing directly to the right. Priya says that if the blade rotates -π/2 radians, then P will be at the lowest point in its circle of rotation." (Lesson 11.1)

**Algebra 2 Unit 7**

* "Priya looks at this histogram of a distribution with a mean of 5.6 grams and a standard deviation of 1.4 grams." (Lesson 8, Practice Problems)
* "Priya is investigating the population density of deer in several forests." (Lesson 15, Practice Problems)
* "Diego rolls a standard number cube 10 times and adds the values to get a sum of 40. Is that unusually high? Priya simulates rolling the number cube 10 times on a computer and adds the values." (Lesson 16, Practice Problems)