Geometry

Question

Geometry

anonymous · Answer

attachment

anonymous · Answer

@phi

phi · Answer

Do you understand what the first statement says?

anonymous · Answer

the theorem or the proof part?

phi · Answer

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 · Answer

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

phi · Answer

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 · Answer

angle 1 = angle 2 because they are vertical angles

phi · Answer

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

anonymous · Answer

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

phi · Answer

what does that mean?

anonymous · Answer

What do you mean?

phi · Answer

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 · Answer

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

phi · Answer

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 · Answer

the trianngles are congruent based on the transitive property

phi · Answer

it does not say that.

anonymous · Answer

the givin angles are congruent by the transitive property?

phi · Answer

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 · Answer

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

phi · Answer

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 · Answer

so its choice B?

phi · Answer

yes.

anonymous · Answer

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

phi · Answer

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...