Geometry 1/2

(x1 + x2)/2 + (y1 + y2)/2

√(x2 - x1)2 + (y2 - y1)2

Logical approach.

Using patterns.

If a conditional, and its hypothesis is true, then so is the conclusion.

If two statements are true, a third can be derived from it.

If p, then q. p → q

If q, then p. q → p

~p → ~q (~ means negative statement)

If not q, then not p. ~q → ~p

p, if and only if q. p ↔ q

If a = b, then a + c = b + c

If a = b, then a - c = b - c

If a = b, then ac = bc

If a = b and c ≠ 0 , then a/c = b/c

Any real number a, a = a

a = b, then b = a

a = b an b = c, then a = c

a = b, a can be used for b in any equation and vice-versa.

If X is on segment AB, and A-X-B (X is between A and B), then AX + XB = AB

Through any two points, there is exactly one line.

If two lines intersect, then they intersect in exactly one point.

Through any three noncollinear points, there is exactly one plane.

If two planes intersect, then their intersection is a line. +

A pair of angles whose sum is 180 degrees.

A pair of angles whose sum is 90 degrees.

Angles that share a common side and vertex.

Angle opposite when two lines cross. These angles are congruent.

Two angles that are adjacent and supplementary.

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

If two are perpendicular, then they intersect to form four right angles.

If two sides of adjacent angles are perpendicular, then the angles are complementary.

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.

Has three equal sides.

Has two equal sides.

Has no equal sides.

Has three angles less than 90 degrees.

Has one angle that is exactly 90 degrees.

Has one angle greater than 90 degrees.

If two angles of one triangle are congruent to two angles of another triangle then the third angles are also congruent.

If two sides of a triangle are congruent, then the angles opposite to them are also congruent.

If two angles of a triangle are congruent, then the sides opposite to them are also congruent.

If a triangle is equilateral, then it is equiangular.

If a triangle is equiangular, then it is equilateral.

If all corresponding sides are congruent in both triangles, then those triangles are congruent.

If two corresponding sides and one corresponding angle of each triangle are congruent to the other.

If two angles and its included side are congruent in both triangles, then both the triangles themselves are congruent.

If two angles and a non-included side are congruent in the two triangles, then both triangles themselves are congruent.

Two right triangles are congruent if the hypotenuse and one leg of one right triangle are congruent to the other right triangle's hypotenuse and leg side.

Once two triangles are proven to be congruent, then every side and angle will also be congruent.

Each side of a triangle has a midpoint. When you connect this midpoint, another triangle can be formed. Each side of this new triangle will be parallel to a side in the overall triangle. This means, that whatever the length of the larger triangle side is, the midsegment counterpart will be half of that + vice-versa.

In a plane, if a point is on the perpendicular bisector of a then it is equidistant from the endpoints of the segment.

In a plane, if a point is equidistant from the endpoints of the segment, then it is on the perpendicular bisector.

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle.

If a point is in the interior of an angle and it is equidistant from the two sides of the angle, then it lies on the bisector of the angle.

The angle bisectors of a triangle intersect at a point that is equidistant from all sides of the triangle.

The centroid of a triangle is located 2/3rds of the distance from each vertex to the midpoint of the opposite side.

The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side.

The lines containing the altitudes of a triangle are concurrent.

If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second.

If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is larger than the third side of the second, then the included angle of the first is longer than the included angle of the second.