Tool Time
The preferred writing utensil in math.
What is a pencil?
Tells us when a straight line (the perpendicular) set up on another straight line makes the adjacent angles equal, each of the angles is right.
What is Definition 10?
Allows us to draw a straight line from any point to any point.
What is Postulate 1?
This allows us to bisect a given finite straight line by first constructing an equilateral triangle ON it.
What is Proposition I.10?
Allows us to conclude that if equals are added to equals, the wholes are equal.
What is Common Notion 2?
A physical tool needed to draw a straight line between two points.
What is a straight edge?
In Proposition I.14, we draw a line that is hypothetically straight with another given line, creating 2 angles that presumably equal ________ right angles.
What is 2?
We commonly call this the Side-Side-Side Theorem.
What is Proposition I.8?
This allows us to draw a straight line at right angles on a given straight line from a point ON the line.
What is Proposition I.11?
Allows us to conclude that things which are equal to the same thing are also equal to one another.
What is Common Notion 1?
The first of two physical tools needed in the construction of an equilateral triangle on a given finite straight line.
What is a compass?
This allows us to draw a straight line at right angles on a given straight line from a point not on the line.
What is Proposition I.12?
Allows us to take any straight line and extend it indefinitely.
What is Postulate 2?
Common Notion 3 tells us that if equals be subtracted from equals, these are equal.
What are remainders?
This Postulate allows us to use our compass to describe a circle with any center and distance.
What is Postulate 3?
This proves that a straight line set upon another straight line makes 2 angles that are either both are right or together equal 2 right angles.
What is Proposition I.13?
If two straight lines are on opposite sides of a given straight line and, meeting at one point of that line, make the adjacent angles equal to two right angles, this allows us to say that that the two straight lines are in a straight line with one another.
What is Proposition I.14?
Common Notions are self-evident and sometimes referred to as __________.
What are axioms?