Proof: opp. angles/sides of parallelogram congruent

[MathedSara]

Hello, hello! Before I start with my question, I just want to say that I'm a junior in college taking advanced geometry. I haven't had geometry since junior year in high school so I cannot for the life of me remember a whole lot about it. So, please help! Thanks


We have to do two proofs:

A parallelogram is defined to be a quadrilateral in which both pairs of opposite sides are parallel. Using the definition (and the property of parallel lines cut b a transversal) to prove the following.

A. Opposite angles of a parallelogram are congruent.
B. Opposite sides of a parallelogram are congruent.

 

[Deleted member 4993]

Hello, hello! Before I start with my question, I just want to say that I'm a junior in college taking advanced geometry. I haven't had geometry since junior year in high school so I cannot for the life of me remember a whole lot about it. So, please help! Thanks


We have to do two proofs:

A parallelogram is defined to be a quadrilateral in which both pairs of opposite sides are parallel. Using the definition (and the property of parallel lines cut b a transversal) to prove the following.

A. Opposite angles of a parallelogram are congruent.
B. Opposite sides of a parallelogram are congruent.

These are very standard theorems - may be corollaries that will be worked out in your text book. Brush up on parallel line theorems.

Draw a diagonal to the parallelogram and apply those theorems.

To start up tell us - what are the properties of parallel lines cut by a transversal.

If you don't have a text book - use google.