Geometry proofs

I hate proofs.

Converse

Exchange hypothesis and conclusion

p—>q

Inverse

Negate both hypothesis and conclusion

~p—>~q

Contrapositive

Switch hypothesis and conclusion then negate both of them  

~q—>~p

Law of detachment

If a hypothesis of a true conditional statement is true then the conclusion is also true

Law of syllogism

If apples, then blueberries

If blueberries then bananas

which means if those statements are both true then

If apples then bananas (is also true)

Two point postulate

Through any two points, there exists exactly one line

Line point postulate

A line contains at least two points.

Line intersection postulate

If two lines intersect, then their intersection is exactly one point.

three point postulate

Through any three noncollinearpoints, there exists exactly one plane.

Plane point postulate

A plane contains at least three noncollinearpoints

Plane line postulate

If two points lie in a plane, then the line containing them lies in the plane

Plane Intersection Postulate

If two planes intersect, then their intersection is a line

Addition property of equality

If two quantities are equal, then adding the same amount to both keeps them equal.

if blueberries = banana then blueberries + apples = bananas +apples

Subtraction property of equality

If two quantities are equal, then subtracting the same amount from both keeps them equal

If blueberries = bananas, then blueberries – apples = bananas – apples.

Multiplication property of equality

If two quantities are equal, multiplying both by the same nonzero number keeps them equal.

If blueberries = bananas, then blueberries × apples = bananas × apples.

Division property of equality

If two quantities are equal, dividing both by the same nonzero number keeps them equal.

If blueberries = bananas, then blueberries ÷ apples = bananas ÷ apples.

Substitution property of equality

If two quantities are equal, either one can be substituted for the other in any expression.

If blueberries = bananas, then you can replace blueberries with bananas in a fruit salad recipe.

Distributive property of equality

Multiplying a number by a sum or difference is the same as multiplying the number by each part separately and then adding or subtracting.

Apples × (blueberries + bananas) = apples × blueberries + apples × bananas.

Apples × (blueberries – bananas) = apples × blueberries – apples × bananas.

Reflexive property

Anything is always equal to itself.

Blueberries = Blueberries

Bananas = Bananas

Apples = Apples.

Symmetric property

If one thing is equal to another, then you can flip them and they are still equal.

If Blueberries = Bananas, then Bananas = Blueberries.

Transitive property

If one thing equals a second, and the second equals a third, then the first equals the third.

If Blueberries = Bananas and Bananas = Apples, then Blueberries = Apples.

Properties of Segment Congruence

Segment congruence (line lengths being the same) is reflexive, symmetric, and transitive.

A blueberry basket is equal to the same blueberry basket.

If a blueberry basket = a banana basket, then the banana basket = the blueberry basket.

If a blueberry basket = a banana basket and a banana basket = an apple basket, then the blueberry basket = the apple basket.

Properties of Angle Congruence

Angle congruence (angles being the same size) is reflexive, symmetric, and transitive.

A blueberry slice of pie is equal to the same blueberry slice of pie.

If a blueberry angle = a banana angle, then the banana angle = the blueberry angle.

If a blueberry angle = a banana angle and the banana angle = an apple angle, then the blueberry angle = the apple angle.

Right Angles Congruence Theorem

All right angles are congruent

Congruent supplements

If two angles are supplementary to the same angle, then those two angles are congruent.

If <1 and <2 are supplementary and <3 and <2 are supplementary, then <1 ≅ <3

Congruent Complements Theorem

If two angles are complementary to the same angle, then those two angles are congruent.

If <4 and <5 are complementary and <6 and <5 are complementary, then <4 ≅ <6

segment addition postulate

If a line of fruit goes from Apple → Banana → Cherry, then the distance from Apple to Banana + the distance from Banana to Cherry = the distance from Apple to Cherry.

Angle addition postulate

If a point is inside an angle, then the two smaller angles add up to the whole angle.

If the banana ray is inside the blueberry angle, then the apple angle + the banana angle = the whole blueberry angle.