Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 14: Quadrilaterals 183

Drawing one diagonal in a parallelogram divides it into two matching triangles. When both
diagonals are drawn in the parallelogram, it makes four triangles. If we call the point where
the diagonals intersect point E, we can show that 'ADE matches 'CBE. AD = BC, because the
opposite sides of the parallelogram are congruent. m’ADE = m’CBE and m’DAE = m’BCE
because the opposite sides are parallel, so alternate interior angles are congruent. That tells
you how to match up the parts of the triangles, and you’ll see the other parts match up as well.
If the triangles are the same size and shape, DE = EB and AE = EC, so the diagonals of the
parallelogram bisect each other.

The family of parallelograms is made up of many different types of parallelograms. Some have
only the properties of parallelograms we’ve covered so far, but others are special in one or more
ways.

D C

A B

E

CHECK POINT

For each quadrilateral described, decide if there is enough information to conclude

that the quadrilateral is a parallelogram.

1. In quadrilateral ABCD, AB CD and BCAD.


2. In quadrilateral PQRS, with diagonal PR, ’QRP # ’SPR and ’QPR # ’SRP.


3. In quadrilateral FORK, ’F # ’K and FO = RK.


4. In quadrilateral LAMP, with diagonals LM and AP intersecting at S,
   'ALS # 'PMS and 'AMS # 'PLS.


5. In quadrilateral ETRA, with diagonals ER and TA intersecting at X, TX = RX
   and EX = AX.