Geometry

- anonymous

Geometry

- katieb

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- anonymous

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- anonymous

- phi

Do you understand what the first statement says?

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- anonymous

the theorem or the proof part?

- phi

I was asking about the first statement of the proof. But now that you mention it, do you understand what the theorem is saying ?

- anonymous

it's saying that if the diagonals split the shape in the center, then its a quadrilateral

- phi

It says if you have a quadrilateral (fancy word for a shape with 4 sides)
and you know its diagonals "bisect each other" (in other words, the point where the diagonals meet is exactly in the center of both diagonals)
then you have a parallelogram (very special: the opposite sides are parallel to each other)
now
Do you understand what the first statement of the proof says?

- anonymous

angle 1 = angle 2 because they are vertical angles

- phi

yes, and that is true.
what about statement 2.

- anonymous

1/2 of each digonal is congruent to its other half because it bisects them

- phi

what does that mean?

- anonymous

What do you mean?

- phi

Just wondering if you know that means if you divide something into 2 equal parts (exactly in half) then the two parts are equal.
ok now statement 3

- anonymous

since 2 sides are equal (congruent) and 1 angle is equal, the two triangles are congruent

- phi

yes, SAS is short for side-angle-side
statement 4. this means, go through the same steps for the 2 other triangles.
it will be true.
now statement 5

- anonymous

the trianngles are congruent based on the transitive property

- phi

it does not say that.

- anonymous

the givin angles are congruent by the transitive property?

- phi

statement 5 says, angle ABD = BDC by the transitive property
I would wonder why we just proved 2 triangles are congruent ? If the angles ABD and BDC are = by the transitive property (what is that ?) then why did we prove triangles are congruent.
on the other hand, if the angles are part of congruent triangles, we could say the angles are equal if they are corresponding parts of congruent triangles.

- anonymous

okay...? so is that the incorrect statement?

- phi

yes, it's not correct. She should have said the angles are equal because they are corresponding parts of congruent triangles (often abbreviated CPCT)

- anonymous

so its choice B?

- phi

yes.

- anonymous

thanks! I think I'm finally starting to understand this proof stuff

- phi

It's tricky, but good to learn how to think logically, so you don't mess up and put on your shoes before you put on your socks...

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