BUILD IT!
Using a given straight line and at a given point on it, a rectilineal angle can be constructed that is _________ to another given rectilineal angle.
What is equal?
In any given triangle, according to Prop. I.20, the sum of any two sides is ____________ ___________ the remaining side.
What is greater than?
Straight lines parallel to the same straight line are also __________________________________.
What is parallel to each other?
In any triangle, the greater side subtends the __________________ ____________.
What is the greater angle?
Two physical tools that Euclid used to draw constructions.
What are the compass and the straightedge?
Proposition I.46 allows us to draw a ____________ on a given straight line.
What is a square?
The three Congruence Theorems, used to determine whether two triangles are congruent.
What are Propositions I.4, I.8, and I.26?
(Or... SAS, SSS, and ASA or AAS?)
If 2 triangles have 2 sides equal to 2 sides respectively, but one has the angle contained by the equal lines greater than the comparative angle, it will also have a greater ___________.
What is base?
In any triangle, the sum of the three interior angles __________ two right angles.
What is equals?
The conclusion of a construction proof.
Q.E.F.
When given a straight line and a point not on it, Proposition I.31 allows us to draw (through the given point) a straight line ______________ to the given line.
What is parallel?
When a smaller triangle is constructed within an existing triangle but shares the same base, the sum of the newly constructed straight lines is _________ than the sum of the two sides of the original triangle.
What is less?
If 2 triangles have 2 sides equal to 2 sides respectively, but one has a greater base than the other, then that angle contained by the equal lines will also be __________________ the comparative angle.
What is greater than?
If a straight line falling on two straight lines makes the alternate angles equal, then the two straight lines are _____________.
What is parallel?
Name of figure that Euclid initially referred to as a "parallelogrammic area"
What is a parallelogram?
In order to construct a triangle out of 3 straight lines, it is necessary that the ________ of any 2 of the lines is greater than the remaining one.
What is sum?
If one of the sides of a triangle is produced, then the ____________ angle equals the sum of the two interior and opposite angles.
What is exterior?
If 2 triangles have 2 angles and 1 side respectively equal, the remaining sides and angle will also be equal, and the triangle is congruent. The abbreviations for the two scenarios that make this true are _______________.
What are ASA and AAS?
If a straight line falling on two straight lines makes the interior angles on the same side equal to two __________ __________, the straight lines will be parallel to one another.
What are right angles?
In a Euclidean proof, this states what is given and what is sought (either to do or to demonstrate - without naming specifics.)
What is the enunciation?
When a smaller triangle is constructed within an existing triangle but shares the same base, the newly constructed straight lines contain an angle that is __________ than the angle contained by the sides of the original triangle.
What is greater?
Props. I.24 and I.25 together say that if 2 triangles have 2 sides equal to 2 sides respectively, then 1 base will be greater than the other base _____________ one of the angles contained by the equal straight lines is greater than the other.
What is iff (if and only if)?
Proposition I.34 proves that the diameter of a parallelogram bisects its area and that _________ sides and angles equal each other.
What is opposite?
A straight line falling on parallel lines makes the interior angles on the same side _________________.
What is equal to two right angles?
The estimated time in history (approximate year) Euclid is believed to have taught.
What is 300 B.C.?