Prove that opposite sides of a parallelogram are congruent. Be sure to create and name the appropriate geometric figures.

Question

anonymous · Answer

Consider the parallelogram http://assets.openstudy.com/updates/attachments/52e74667e4b096fa405b41e8-yttrium-1390888812280-1.jpg

anonymous · Answer

Thru definition, we know that AB || CD and BD || DA

anonymous · Answer

We are to prove that  AB = CD and BD = DA
Then let AC be the diagonal of the parallelogram

anonymous · Answer

Consider two triangles ABC and CDA as the figure we had.
In triangles, 
1. <CBA = <ACD (the line AC is a transversal of parallel lines AB and CD,hence Angle CAB and ACD are alternate angles) 
2. <ACB=<CAD (The line AC is a transversal of parallel lines BC and DA,hence Angle ACB and Angle CAD are alternate angles) 
3. AC=CA (The common side to two triangles)

anonymous · Answer

From conditions 1,2 and 3, 
Triangles ABC and CDA are congruent (By Angle -Side-Angle congruency property) 
Hence as triangles are congruent triangles , the corresponding sides are equal, 
Hence, AB = CD and BC = DA.

leahhhmorgannn · Answer

Thing is, if you're going to explain this, it's probably best to start from the beginning because I'm not even sure what a parallelogram IS

anonymous · Answer

so the answer will be Consider two triangles ABC and CDA as the figure we had.
In triangles, 
1. <CBA = <ACD (the line AC is a transversal of parallel lines AB and CD,hence Angle CAB and ACD are alternate angles) 
2. <ACB=<CAD (The line AC is a transversal of parallel lines BC and DA,hence Angle ACB and Angle CAD are alternate angles) 
3. AC=CA (The common side to two triangles) 
From conditions 1,2 and 3, 
Triangles ABC and CDA are congruent (By Angle -Side-Angle congruency property) 
Hence as triangles are congruent triangles , the corresponding sides are equal, 
Hence, AB = CD and BC = DA.

anonymous · Answer

A parallelogram is a shape... Like this one: http://assets.openstudy.com/updates/attachments/52e74667e4b096fa405b41e8-yttrium-1390888812280-1.jpg

anonymous · Answer

Hope this helped! Have a great day! @leahhhmorgannn

leahhhmorgannn · Answer

See, I have no idea what any of what you just posted even means. Or how to read it. 
So that's completely unhelpful. Thanks for nothing.

leahhhmorgannn · Answer

@Data_LG2

leahhhmorgannn · Answer

@Mehek14