Question

Look at the figure shown below:

Answer 1

A student made the table below to show the steps to prove that DC is equal to EC:

Answer 2

A. Provide the missing statement and justification in the proof.
B. Using complete sentences, explain why the proof would not work without the missing step.

Answer 3

Can anyone help me? I'm confused here.

Answer 4

Look at the statements \(4\) and \(5\)

Answer 5

right hand sides are same for the equations in those statements, yes ?

Answer 6

Yes

Answer 7

mistake, i meant statements \(4\) and \(6\)

Answer 8

They are different, except for the last one, which is DCE

Answer 9

take a good look again at statemetns 4 and 6

Answer 10

i have circled them in red in above attachment

Answer 11

Angle BCD is the only different one.

Answer 12

More importantly, notice that the right hand sides are equal. So the left hand sides also must be equal. Can we say :
\[7. ~m\angle ACE = m\angle BCD~~~~\text{By transitive property } \]

?

Answer 13

thats the statement and justification that can go in the 7th line

Answer 14

Oh, I see what you mean

Answer 15

Now, why would the proof not work without the missing step?

Answer 16

thats for part A

Answer 17

for part B put something like below :
The proof would not work without the missin step because for ASA postulate we need we need two angle pairs and an included pair to be congruent to each other. At step8 ASA postulate is used but only one pair of angle and side were proven to be congruent till that step. So ASA postulate would not work at step8 if the step7 line is left empty

Answer 18

add as many sentences as possible and explain everything you know

Answer 19

Alright, thnx so much!
Do you think you can help me on another question I have, @ganeshie8?

Answer 20

sure ask