Question

Look at the figure shown below.

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

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 1

@ganeshie8

Answer 2

look at the next step, they're using ASA to prove triangles are congruent.

so we need another angle to pull off ASA here

Answer 3

look at 4th and 6th rows and tell me what can we conclude ?

Answer 4

m∡ACE = m∡ACD + m∡DCE and m∡BCD = m∡ACD + m∡DCE

Answer 5

yeah what can we conclude from that

Answer 6

m∡ACE = m∡BCD

Answer 7

perfect put that in the balnk

Answer 8

Justification : Substitution

Answer 9

How is it substitution?

Answer 10

tell me how is it substitution in row 6

Answer 11

m∡ACE was subsituted with m∡BCD

Answer 12

same thing here also.

Answer 13

m∡ACD + m∡DCE was substituted with m∡BCD

Answer 14

That kind of makes sense.

Answer 15

you can put "Transitive property of equality" also for this Justification. Both will work. Upto you how you see it.

Answer 16

On second thoughts, I prefer "Transitive property of equality" for this to Substitution

Answer 17

Okay, can you explain to me how it wouldn't work without this missing step?

Answer 18

@ganeshie8

Answer 19

keep it simple : without the missing step, the proof would not work cuz oly one Angle and one Side are proven congruent. So ASA will not work.

Answer 20

Than you!

Answer 21

np :)