Question

May you help me with this problem?
@mathstudent55

Answer 1

Notice
I states BGCH is a parallelogram. The reason is opp sides are parallel.

Nothing has been stated yet about parallel sides, so I cannot be the first of these statements.

Answer 2

Also notice
II uses a property of a parallelogram, so it's logical that II must follow I

Answer 3

Meaning, II is also out- correct?

Answer 4

The first of the statements must be IV.
From the figure and the construction, you can state IV.

Answer 5

It is between B and D then.

Answer 6

IV, III, I, II

Answer 7

If you want, I'll explain it to you.

Answer 8

Why wouldn't it be "D" , I thought I went last?

Answer 9

No. They used it the other way.
The definition of a parallelogram is:
A parallelogram is a quadrilateral that has two pairs of parallel opposite sides.

Answer 10

You agree with that definition?

Answer 11

Yes.

Answer 12

A definition can be used two ways in a proof.
If one statement of a proof states a quadrilateral is a parallelogram, then using the definition, you can state the opposite sides are parallel.
That is one way of using the definition.

Answer 13

The other way of using the definition is:
If you state that a quadrilateral has both pairs of opposite sides parallel, you can use the definition to state the quadrilateral is a parallelogram.

Answer 14

In other words a definition works both ways.

Answer 15

This is not the case with a theorem or a postulate.

Answer 16

For theorems and postulates, the converses must be either proved (in the case of a theorem) or a new postulate must be assumed (in the case of a postulate.)

Answer 17

I can go over this step by step to show the logic of the order of the steps.

Answer 18

II is similar to CPCTC.
Do you know CPCTC for congruent triangles?

Answer 19

corresponding parts of congruent triangles are congruen , yeah

Answer 20

congruent*

Answer 21

Right.
How do you use CPCTC?
Let's say you need to prove two segments are congruent.
It just so happens that the segments are corresponding parts of two triangles.
If you can show the triangles are congruent, then you can state the segments are congruent by CPCTC.

Answer 22

In our case, we want to show that seg. BD is congruent to seg. DC.
If we prove quad. BGCH is a parallelogram, then we can use the property of parallelograms that their diagonals bisect each other to state that seg. BD is congruent to seg. DC.

Answer 23

That is why statement II must follow statement I.
In statement I we prove BGCH is a parallelogram.
In statement II we draw a conclusion from the fact that BGCH is a parallelogram.

Answer 24

We used statements IV and III to prove BGCH is a parallelogram.
That means statements IV and III must come before statement I.

Answer 25

Now between statements IV and III, how do you know which one comes first?

Answer 26

Statement IV comes first (before statement III), because from the figure you have, you can conclude the statement of statement IV.

Answer 27

Thank you soo much for condensing this information, sometimes it's so intimidating and you just make it so much more clearer and understandable than what it really is.. :D

Answer 28

!!!!*

Answer 29

You're welcome.
Statement IV comes directly from info you already have before these 4 steps you have to put in order.

Answer 30

Ah. I have 3 more that I don't get. May I tag you in them as well?

Answer 31

Sure.

Answer 32

For statement IV, look at triangle ABH.
We already know AF = FB
We also know AG = GH
From that info we use the midsegment theorem to state FG is parallel to BH.

We do a similar thing with triangle AHC to get GE parallel to HC.

This is all statement IV which comes from statements we already have above.

Then by substitution we do statement III.

Then we do statements I and II in that order.