Propositions
The given for proposition 1.
What is a straight finite line AB.
That all right angles are equal to one another
What is Postulate 4?
To place at a given point as an extremity a straight line equal to a given straight line.
What is Prop 2?
Prop 1 given
What is a finite straight line?
Please describe to me how you bisect an infinite line?
What is "You don't."
These are the four propositions to prove triangles are congruent to one another.
What is SAS, SSS, ASA, and AAS?
This common notion can be used for "substitution" in proofs, and its definition.
What is common notion 1- two things equal to the same thing are equal to one another.
Prop 10 lets us do this
What is bisect a given finite straight line?
Prop 9 to prove
What is to bisect a given rectilineal angle
When two lines intersect it always makes the _________ equal to one another.
What is vertical angles.
This is the proposition lovingly known as "Pons Asinorum"
What is the proposition proving that in isosceles triangles the base angles are equal, as are the angles under the base.
A straight line falling on another straight line.
What creates two angles equal to the sum of two right angles?
These propositions show Side Angle Side Theorem and Side Side Side Theorem.
What are props 4 and 8?
You're given a triangle with two equal angles in this prop
What is prop 6?
What is the smallest rectilinear angle?
What is none.
Proposition 41
What is the proposition that proves a parallelogram is twice the area of the triangle that has the same base and height (or lies within the same parallel lines)?
Postulate 3
What is to describe a circle with any centre and distance?
These two propositions are converses of one another
What are props 5 and 6?
We prove this in prop 16
How does a "Reductio ad absurdum" argument work?
What is a an argument that is proven by producing false statements to come to the correct statement.
This is a Taxi Circle.
What is the sum of all points equal distant from a center point moving only at straight lines and right angles?
This is the difference between Common Notions 1 and 4.
What is that CN 4 has two things that coincide, or can overlap each other, while CN1 involves identities of things- two items which are equal to another or third thing, are then equal to each other.
Prop 12 is the first time we formally encounter this in a proof.
What is the infinite?
When proving this prop, you also prove a porism. Double the points if you can state the porism.
What is prop 15? Porism: If two straight lines cut one another they will make the angles at the point of section equal to four right angles
What is Prop 13 proving?
What is "If a straight line set up on a straight line makes angles, it will make either two right angles or angles equal to two right angles?"