Noah

> I constructed 2 perpendicular bisectors of triangle ABC. That means the point where they intersect is the circumcenter!
>
> Noah, Geometry Unit 7, Lesson 5 Practice Problems

**Noah** is one of the more introverted characters. He is dating Jada, and although she cheated on him with Andre at some point, he likely does not know this. He is also friends with Priya, who he likes to play Invisible Triangles and ride Ferris wheels with. Other than that, he avoids doing math problems with others when he can.

The only interesting details about Noah are that he likes juice and that he is the editor for the school newspaper. Also, he seems to be skilled in sculpting, photography, and perhaps programming.

## Notable Appearances

**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.*

**Geometry Unit 5**

* "Noah edits the school newspaper. He is planning to print a photograph of a flyer for the upcoming school play." (Lesson 7, Practice Problems)

*Analysis: This confirms that Noah is the editor for the school newspaper.*

* "Noah is deciding which of 2 juice containers he should buy." (Lesson 10, Practice Problems)

*Analysis: This confirms that Noah likes juice.*

**Geometry Unit 7**

* "Priya and Noah are riding different size Ferris wheels at a carnival. They started at the same time." (Lesson 11, Practice Problems)

*Analysis: This supports the theory that Noah and Priya are friends, and confirms that Noah likes Ferris wheels.*

* "Noah is taking photos of a sculpture he made in art class. He will submit the photos to a contest. The sculpture is in front of a backdrop, which is represented from an overhead view in the image by segment AB. Noah positioned a light at point C so that the edges of the light beam meet up exactly with the backdrop at segment AB. Noah wants to try different positions for the light to highlight different aspects of the sculpture, but he still wants the edges of the beam to exactly meet the endpoints of the backdrop." (Lesson 14.4)

*Analysis: This confirms that Noah is both a sculptor and a photographer.*

**Algebra 2 Unit 6**

* "Jada, Noah, and Elena are riding a carousel. The carousel moves in a counterclockwise direction. When the ride begins, Jada is at position J, Noah is at position N, and Elena is at position E." (Lesson 18.2)

*Analysis: Confirms that Noah is friends with Jada and Elena, because they spend time together outside of school.*

* Jada begins the carousel ride at point J and Noah begins the carousel ride at point N. The radius of the carousel is 20 feet and it rotates in a counterclockwise direction, making one complete rotation every 10 seconds." (Lesson 18.3)

*Analysis: Reinforces the idea that Noah is friends with Jada.*

**Algebra 2 Unit 7**

* "Noah writes a computer program to recombine all the data into 12,870 possible different groupings and finds that 2,612 of the different groupings have a difference in means of at least 0.6 part per million." (Lesson 15, Practice Problems)

*Analysis: Noah is good with technology.*

## Miscellaneous Appearances

**Geometry Unit 1**

* "Noah is trying to bisect angle BAC. He draws circles of the same radius with centers B and C and then uses one of the points of intersection for his ray." (Lesson 7, Practice Problems)
* "Noah says that a 180 degree rotation, with center P, has the same effect on points in the plane as reflection over line m." (Lesson 11, Practice Problems)
* "Noah starts with triangle ABC and makes 2 new triangles by translating B to A and by translating B to C. Noah thinks that triangle DCA is congruent to triangle BAC." (Lesson 22, Practice Problems)

**Geometry Unit 7**

* "Noah says, 'I constructed 2 perpendicular bisectors of triangle ABC. That means the point where they intersect is the circumcenter!' Andre responds, 'No, we still need to check the third perpendicular bisector to make sure it intersects at the same point.'" (Lesson 5, Practice Problems)
* "Noah makes 3 statements about the incenter of a triangle." (Lesson 14, Practice Problems)

**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.'" "Noah's approach: In the Isosceles Triangle Theorem Proof, Mai and Kiran drew an angle bisector in their isosceles triangle, so I'll try that. I'll draw the angle bisector of ACB. The point where the angle bisector hits AB will be D. So triangles ACD and BCD are congruent, which means AD and BD are congruent, so D is a midpoint and CD is the perpendicular bisector.'" (Lesson 8.2)
* "Noah wrote a proof to show that triangle HEG is congruent to triangle FEG." (Lesson 10, Practice Problems)

**Algebra 2 Unit 3**

* "Noah solved the equation 5x^2 = 45. Here are his steps." (Lesson 7, Practice Problems)
* "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)
* "Noah uses the quadratic formula to solve the equation 2x^2 + 3x - 5 = 4." (Lesson 16, Practice Problems)

**Algebra 2 Unit 5**

* "Jada thinks changing the equation to J(t) = -62(0.85)^t + 75.1 makes a good model for the data. Noah thinks N(t) = -62(0.85)^(t-1) + 68 is better." (Lesson 3.3)

**Algebra 2 Unit 7**

* "Noah and Clare are studying the noise level, in decibels, outside of their school in the morning." (Lesson 12, Practice Problems)