Diego

> To find arc length, divide the measure of the central angle by 360. Then multiply that by the area of the circle.
>
> Diego, Geometry Unit 7, Lesson 8

**Diego** is extremely extroverted. He loves to work on math problems with other people, and the only character he is never seen with is Han. Other things that are known about him are that he is good at photoshop, he likes juice, and he likes stacking pennies, as well as collecting coins in general. Also, he plays basketball, although he isn't very good at it. Diego is good friends with Priya, Elena, Clare, and Andre, although he's not dating anyone.

## Notable Appearances

**Geometry Unit 3**

* "Diego took a picture of a hippo and then edited it." (Lesson 1.1)

*Analysis: This confirms that Diego is good at photoshop.*

**Geometry Unit 5**

* "Diego is deciding which of 2 juice containers he should buy." (Lesson 18, Practice Problems)

*Analysis: This confirms that Diego likes juice.*

**Algebra 2 Unit 1**

* "Diego is making a stack of pennies. He starts with 5 and then adds them 1 at a time. A penny is 1.52 mm thick." (Lesson 9, Practice Problems)

*Analysis: This confirms that Diego likes stacking pennies.*

**Algebra 2 Unit 5**

* "Diego discovers that the temperature inside the oven is always 25 degrees warmer than the oven's temperature setting." (Lesson 2, Practice Problems)

*Analysis: Diego either likes baking, or just ovens in general. Evidence is intriguing but inconclusive.*

**Algebra 2 Unit 7**

* "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: Diego plays basketball, although he isn't great at it.*

* "Diego has a jar containing 36 coins." (Lesson 9.1)

*Analysis: This confirms that Diego collects coins.*

## Miscellaneous Appearances

**Geometry Unit 1**

* "Diego says a quadrilateral with 4 congruent sides is always a regular polygon. Mai says it is never one." (Lesson 11, Practice Problems)
* "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 17.3)
* "Diego makes the conjecture: 'The angle formed by the angle bisectors is always a right angle, no matter what the angle between r and l is.'" (Lesson 19.2)

**Geometry Unit 2**

* "Diego, Jada, and Noah were given the following task: Prove that if a point is the same distance from A as it is from B, then C must be on the perpendicular bisector of AB. At first they were really stuck. Noah asked, 'How do you prove a point is on a line?' Their teacher gave them the hint, 'Another way to think about it is to draw a line that you know C is on, and prove that line has to be the perpendicular bisector.'" "Diego's approach: 'I drew a line through C that was perpendicular to AB and through the midpoint of AB. That line is the perpendicular bisector or AB and C is on it, so that proves C is on the perpendicular bisector.'" (Lesson 8.2)
* "Diego states that diagonal WY bisects angle ZWX and ZYX," (Lesson 12, Practice Problems)

**Geometry Unit 3**

* "Elena is playing with the equivalent ratios she wrote in the warm-up. She rewrites a/x = c/a and a^2 = xc. Diego notices and comments, 'I got b^2 = yc. The a^2 and b^2 remind me of the Pythagorean Theorem.' Elena says, 'The Pythagorean Theorem says that a^2 + b^2 = c^2. I bet we could figure out how to show that.'" (Lesson 14.2)

**Geometry Unit 6**

* "Elena is writing an explanation on completing the square for circle equations for Diego because he missed class. Here is what Elena wrote: 'Suppose we want to rewrite an equation in the form (x - h)^2 + (y - k)^2 = r^2. First, move any numbers to the right side and group terms with the same variables together on the left. Second, figure out what must be added to the set of -terms and the set of -terms to create 2 perfect square trinomials. Add those numbers to both the left and right sides of the equation. Next, rewrite the perfect square trinomials as squared binomials, and rewrite the right side in the form r^2. The center and radius can now be read directly from the equation.' Diego is unsure how to determine what needs to be added in order to get 2 perfect square trinomials." (Lesson 14, Practice Problems)

**Geometry Unit 7**

* "Diego says, 'No matter where we put point D, the Pythagorean Theorem tells us that segment CJ is shorter than segment CD. So, segment CJ represents the shortest path to shore.'" (Lesson 3.1)
* "Diego says, 'To find arc length, divide the measure of the central angle by 360. Then multiply that by the area of the circle.'" (Lesson 8, Practice Problems)
* "Clare and Diego are discussing inscribing circles in quadrilaterals. Diego thinks that you can inscribe a circle in *any* quadrilateral since you can inscribe a circle in any triangle. Clare thinks it is not always possible because she does not think the angle bisectors are guaranteed to intersect at a single point. She claims she can draw a quadrilateral for which an inscribed circle can’t be drawn." (Lesson 9, 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)
* "Andre and Diego are each saving money. They each hope to save 500 dollars. They are tracking their progress on the circles in the image. Diego thinks that Andre has saved more money than Diego has saved. Andre thinks they have saved the same amount." (Lesson 13, Practice Problems)

**Algebra 2 Unit 2**

* "Diego wrote f(x) = (x + 2)(x - 4) as an example of a function whose graph has x-intercepts at x = -4, 2." (Lesson 7, Practice Problems)
* "Diego used the long division shown here to figure out that 6x^2 - 7x - 5 = (2x + 1)(3x - 5)." (Lesson 13.2)

**Algebra 2 Unit 3**

* "Diego saw Clare's work and said, 'Now I'm wondering about 3^1/2.' First he graphed y = 3^x for some whole number values of x, and estimated 3^1/2 from the graph." (Lesson 3.2)
* "Diego squared a number and got 4. Andre squared a different number and got 4." (Lesson 11, Practice Problems)

**Algebra 2, Unit 4**

* "Diego says that the expression ln5 represents the time, in years, when the account will have 5 thousand dollars." (Lesson 15.2)

**Algebra 2 Unit 5**

* "Andre says that g(x) = 0.1x(0.1x - 5)(0.1x + 2)(0.1x + 5) is obtained from f by scaling the inputs by a factor of 0.1. Clare says this graph is a vertical shift of the graph of f down 100 units. Diego says the graph of k(x) = -x(x - 5)(x + 2)(x + 5) is the reflection of the graph over the y-axis." (Lesson 9, Practice Problems)

**Algebra 2 Unit 7**

* "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)