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Day 13 ­ Proving that a quad is a rectangle or rhombus

We already looked at how to prove that a quad is a parallelogram:
   both pairs opp sides ||
   both pairs opp sides ≅
   one pair opp sides both || and ≅
   both pairs opp angles ≅
   diagonals bisect each other

          The      symbol is only used for parallelogram.
In order to prove that a quadrilateral is a rectangle or rhombus,
  YOU MUST FIRST SHOW THAT IT IS A PARALLELOGRAM.

Then, it only takes one more condition to make it a rectangle or rhombus.

   A    with ≅ diagonals          rectangle
   A    with one rt angle         rectangle

   A    with     diagonals     rhombus
   A    with one pair consecutive ≅ sides    rhombus
   A    with a diagonal that bisects opposite angles            rhombus
Example Proof:
   A             B   Given:   AD    DC
                              BC   DC
                              AD ≅ BC

   D             C   Prove:  ABCD is a rectangle

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Lsn 11-8: Proving a Rhombus/Rectangle