Midterm Flashcards
Proposition 13
Line on a line will create angles equal to two right angles
Proposition 14
If a line intersects a line and create two right angles, the lines are perpendicular
Proposition 15
Vertical angles are equal
Define alternate angles
Vertical angle on a different parallel line traversed by the same line
Proposition 27
If a line traverses two lines such that the alternate angles are equal, the lines are parallel.
Proposition 28
If a straight line falling on two straight lines make the exterior angle equal to the interior and opposite angle on the same side, or the interior angles on the same side equal to two right angles, the straight lines will be parallel to one another.
Proposition 29
A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle equal to the interior and opposite angle, and the interior angles on the same side equal to two right angles.
Book 1, Proposition 34
In parallelogrammic areas the opposite sides and angles equal one another, and the diameter bisects the areas.
Book 1, Proposition 35
Parallelograms which are on the same base and in the same parallels are equal to one another.
Book 1, Proposition 36
Parallelograms which are on equal bases and in the same parallels are equal to one another.
Book 1, Proposition 37
Triangles which are on the same base and in the same parallels are equal to one another.
Book 1, Proposition 38
Triangles which are on equal bases and in the same parallels are equal to one another.
Book I, Proposition 41
If a parallelogram has the same base with a triangle and is in the same parallels, then the parallelogram is double the triangle.
I.47, “Pythagorean Theorem”
In right-angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle.
Book 1, Proposition 48
If in a triangle the square on one of the sides equals the sum of the squares on the remaining two sides of the triangle, then the angle contained by the remaining two sides of the triangle is right.
