Show:
Descriptions of Points and Lines
Graph Theory
The Dimensions
Segment Distance
The Triangle Inequality
100
This type of letter is used to name a point in a diagram.
What is a capital letter? (Example: Point R)
100
These are the descriptions of "point" and "line" in graph theory.
What are... "Point" - a node of a network. "Line" - an arc connecting two nodes or one node to itself.
100
This is the 0-Dimension
What is a point (or "location")?
100
This is how you would name the segment in Picture 4A on the overhead. Draw the correct symbol!
What is segment EG? (EG with a bar on top, no arrows)
100
This is what the triangle inequality tells us.
What is that two smaller sides of a triangle must add up to more than the third side?
200
These are the two ways you can name a line.
What are (1) by any two points on the line and (2) by a lowercase letter? Example: Line AB(with a double-sided arrow above AB) or line m
200
This is what it means for a network to be "traversable".
What is... You can trace through every arc exactly once without picking up your pencil or crossing an arc twice? Also acceptable: No more than two ODD nodes in a network.
200
This is the 1st dimension.
What is a line (or "length")?
200
This is the definition of a ray.
What is... an object with an endpoint at one point and extending infinitely in one direction "through" another point on the line?
200
This is a possible third side to the triangle with two sides 3 and 6.
What is 4,5,6,7,or 8?
300
This is the description of "a point" and "a line" according to discrete geometry. (need to give both descriptions)
What is "a dot" (for "point") and "a set of dots in a row" (for "line")?
300
This is the description of the difference between an odd and an even node.
What is.. Odd node - has an odd number of arcs extending from it. Even node - has an even number of arcs extending from it.
300
This is the definition of "coplanar".
What is the term used to describe points and lines that are all on the same 2-dimensional plane?
300
This is the explanation to whether or not ray DR and ray TR are opposite rays.
What is... No, because they do NOT share the same endpoint. The endpoint of ray DR is D, while the endpoint of ray TR is T. Opposite rays need to share the same endpoint and extend in exact opposite directions.
300
This is the length of the third side of a triangle that is NOT possible with side lengths 6 and 10
What is any number less than or equal to 4 or greater than or equal to 16?
400
In discrete geometry, explain whether or not two lines necessarily cross when they intersect, and explain why or why not.
In discrete geometry, lines are defined as a set of dots in a row, so there could be space in between the dots. Therefore, lines that "cross" do NOT necessarily "intersect".
400
This is the solution to Euler's Bridge Problem. (FULL Explanation needed)
What is... There is no solution! It is not traversable, because there are more than two odd nodes in the network.
400
This is an example of how "circularity" works.
What is (answers will vary, discretion given to teacher)...?
400
In figure 4D, this is the value of x. (show all steps)
What is 13?
400
This is what the triangle inequality tells us about triangle ABC symbolically. (Choose one correct response) a. AB+BC>BC b. BC+AC>AB c. AC>AB+BC d. AB+BC=AC
What is (b) BC+AC>AB
500
This is the difference between Euclidean Synthetic Geometry and Euclidean Coordinate Geometry when describing a point.
What is... Euclidean Synthetic Geometry - A point is an exact location. Euclidean Coordinate Geometry - A point is an ordered pair of real numbers.
500
Referring to Picture #2E on the overhead, this is the answer to whether or not the network is traversable. (FULL Explanation needed)
What is... Yes! It is traversable, because it has no more than two odd nodes.
500
These are the three different parts to the "point-line-plane postulate".
What are... 1. Through any two points there is exactly one line. 2. You can create a number line out of any line and the points on that line. 3. To create the next dimension, you need to find a point outside of the current dimension. (similar answer)
500
This is the length of segment AB in picture 4E on the overhead.
What is 34?
500
This is your correct evaluation of picture of 5E.
What is that this is a valid triangle by the triangle inequality postulate?