Proving Quadrilateral Properties

1
Proving Quadrilateral Properties

• Sometimes working backwards can help to solve a
  problem
• Which fire hydrant should be turned on?
• Did you trace back from the nozzle?

• Heres another example
• Start at square 1 and end at square 100 by
  finding a path through adjacent squares
  horizontally, vertically, or diagonally
• You can only move to a square if you can add,
  subtract, multiply, or divide the number in the
  current square by 2 or 5 to get the number in
  that square

2
Proving Quadrilateral Properties

• This approach can also be helpful when writing
  proofs
• Begin with what is to be proven
• Think of ways that statement might be proven
• Back up one level and see how that statement can
  be proven
• If you get to a point where congruent triangles
  would help, see if you can identify the triangles
  on the diagram
• Look at what is known about the triangles and see
  if any other facts can be show to prove that they
  are congruent

A dart is a concave kite
Given Dart ADBC with CA _at_ CB and DA _at_
DB Show CD bisects ÐACB
3
Proving Quadrilateral Properties

• Want to prove that CD bisects ÐACB
• For that to be true, ÐACD must be congruent to
  ÐBCD
• Those angles would be congruent if DACD and
  DBCD are congruent
• The givens list two congruent sides, so
  look for SAS or SSS congruence
• CD is a shared side, so its congruent to itself
• That makes SSS work for DACD and DBCD

Given Dart ADBC with CA _at_ CB and DA _at_
DB Show CD bisects ÐACB