At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
Do you understand what the first statement says?
the theorem or the proof part?
I was asking about the first statement of the proof. But now that you mention it, do you understand what the theorem is saying ?
it's saying that if the diagonals split the shape in the center, then its a quadrilateral
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?
angle 1 = angle 2 because they are vertical angles
yes, and that is true. what about statement 2.
1/2 of each digonal is congruent to its other half because it bisects them
what does that mean?
What do you mean?
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
since 2 sides are equal (congruent) and 1 angle is equal, the two triangles are congruent
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
the trianngles are congruent based on the transitive property
it does not say that.
the givin angles are congruent by the transitive property?
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.
okay...? so is that the incorrect statement?
yes, it's not correct. She should have said the angles are equal because they are corresponding parts of congruent triangles (often abbreviated CPCT)
so its choice B?
thanks! I think I'm finally starting to understand this proof stuff
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...