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Geo Final Cheat Sheet (DRAFT) by

This is a draft cheat sheet. It is a work in progress and is not finished yet.

6-1

Polygon Angle Sum Theorum
the sum of the measures of the interior angles of an n-gon is (n-2)180 each vertex, is 260
Corollary to the Polygon Angle­ Sum theorem
The measure of each interior angle of a regular n­gon is (n­2)180/n
Polygon Exterior Angle­ Sum theorem
The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360

6-2

Parall­elo­gram­
quadri­lateral with both pairs of opposite sides parallel
In a quadri­lat­eral, opposite sides do not share a vertex and opposite angles do not share a side
Theorem 6­-3
If a quadri­lateral is a parall­elo­gram, then its opposite sides are congruent
Theorem 6-4
If a quadri­lateral is a parall­elo­gram, then its consec­utive angles are supple­mentary
Theorem 6-5
If a quadri­lateral is a parall­elo­gram, then its opposite angles are congruent
Theorem 6-6
If a quadri­lateral is a parall­elo­gram, then its diagonals bisect each other

Theorem 6-7

6-3

Theorem 6­-8
If both pairs of opposite sides of a quadri­lateral are congruent, then the quadri­lateral is a parall­elogram
Theorem 6-9
If an angle of a quadri­lateral is supple­mentary to both its consec­utive angles, then the quadri­lateral is a parall­elogram
Theorem 6-10
If both pairs of opposite angles of a quadri­lateral are congruent, then the quadri­lateral is a parall­elogram
Theorem 6-11
If the diagonals of a quadri­lateral bisect each other, then the quadri­lateral is a parall­elogram
Theorem 6-12
If one pair of opposite sides of a quadri­lateral is both congruent and parallel, then the quadri­lateral is a parall­elogram

6-4

Rhombus­
parall­elogram with 4 congruent sides
Square­
parall­elogram with 4 congruent sides and 4 right angles
Rectangle­
parall­elogram with 4 right angles
Theorem 6-13
If a parall­elogram is a rhombus, then its diagonals are perpen­dicular
Theorem 6-14
If a parall­elogram is a rhombus, then each diagonal bisects a pair of opposite angles
Theorem 6-15
If a parall­elogram is a rectangle, then its diagonals are congruent

6-5

Theorem 6­-16
If the diagonals of a parall­elogram are perpen­dic­ular, then the parall­elogram is a rhombus
Theorem 6-17
If one diagonal of a parall­elogram bisects a pair of opposite angles then the parall­elogram is a rhombus
Theorem 6-18
If the diagonals of a parall­elogram are congruent, then the parall­elogram is a rectangle