Geometric Theorems
A few theorems to use in geometric proofs.
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- AEA Theorem
- alternate exterior angles of a transversal are congruent
- Vertical Angle theorem
- vertical angles are congruent
- NASP Theorem
- Non-adjacent sides of a parallelogram are congruent
- Exterior Angle Theorem
- The sum of two angles of a triangle is equal to the exterior angle of the remaining angle
- Transitive Property
- If a = b and b = c, then a = c
- Quadrilateral Sum Theorem
- The angles of a quadrilateral add up to 360 degrees
- AIA Theorem
- alternate interior angles of a transversal are congruent
- Reflexive Property
- any number is equal to itself
- Substitution Property
- If a+b=c and b=d, then a+d=c
- Isoceles Base Angle Theorem
- The base angles of an isoceles triangle are congruent
- Line Postulate
- It is possible to construct exactly one line through any two points
- Midpoint Postulate
- It is possible to construct exactly one midpoint on any line
- Polygon Sum Theorem
- If n = the # of sides, the number of degrees in a polygon is 180n-360
- Isoceles Mega Theorem
- The altitude from the top vertex of an isocleles triangle is also a median, an angle bisector, and a perpendicular bisector
- CA Postulate
- In a transversal, the corresponding angles are congruent
- SSIA Theorem
- interior angles on the same side of a transversal add up to 180 degrees
- NAAP Theorem
- Non-adjacent angles of a parallelogram are congruent
- Triangle Sum Theorem
- the angles of a triangle add up to 180 degrees