Proof Builder

Project for HackTech 2016.

Points

A Point is a geometrical point defined by a single letter.

Point(Object):

    char name

Line Segments

A LineSegment is defined by two Point objects.

LineSegment(Object):

    Point start
    Point end

    # Initially null.
    Point midpoint

Triangles

A Triangle is an object with three Point objects.

Triangle(Object):

    Point point_1
    Point point_2
    Point point_3

    LineSegment side_1
    LineSegment side_2
    LineSegment side_3

Congruence

A Congruence is an equality relationship between two other objects.

Congruence:

    Object object_1
    Object object_2

TriangleCongruence(Congruence):

    Triangle tr_1
    Triangle tr_2

    # Sides of each triangle such that corresponding indices indicate congruence.
    Array tr_1_sides
    Array tr_2_sides

Theorems

A Theorem applies its method to objects that satisfy the conditions.

Theorem:

    # Returns true iff OBJS satisfy the conditions.
    boolean checkCondition(Object... objs)

    # Applies the result of the theorem to OBJS.
    void applyResult(Object... objs)

Starter Theorems

Reflexive Property

• Objects: LineSegment l
• Conditions:
  • None
• Results:
  • Creates Congruence(l, l)

Midpoint Splitting Theorem

• Objects: LineSegment
• Conditions:
  • obj.midpoint is not null
• Results:
  • Creates l1 = LineSegment(obj.start, obj.midpoint)
  • Creates l2 = LineSegment(obj.midpoint, obj.end)
  • Creates Congruence(l1, l2)

SSS Postulate

• Objects: Triangle tr1, Triangle tr2
• Conditions:
  • For every side1 of tr1, there exists a side2 of tr2 such that there exists Congruence(side1, side2)
• Results:
  • Creates TriangleCongruence(tr1, tr2) with the corresponding sides

Proving Theorems

Exercise 1: SSS

• Given: Triangle ABD, Triangle CBD, AC.midpoint = B
• Goal: Congruence(ABD, CBD)