Bonus Proof

[vampirewitchreine]

So this is an extra credit thing, with no set amount of statements and reason.



Given: segment AB is congruent to segment BC
segment DE is congruent to segment EC
Prove: angle A is congruent to angle D


(Below is the proof that I have worked out so far)

Statement	Reason
1. segment AB is congruent to segment BC	1. Given
2. angle ECD is congruent to angle BCA	2. Vertical angles are congruent
3. segment DR is congruent to segment EC	3. Given

What should my next step be? Do I need to have one more step before I prove angle A is congruent to angle D or can I go ahead and prove it somehow?

 

[pka]

You have two isosceles triangles. Think base angles.
Also a pair of vertical angles.

 

[vampirewitchreine]

You have two isosceles triangles. Think base angles.
Also a pair of vertical angles.

I forgot that I'd posted this ages ago..... I came across it again as I was getting my papers in order to send off to my teacher




After the parts of my proof that I already submitted I have:

4. angle C is congruent to angle D	4. Base angles of an isosceles triangle are congruent
5. angle C is congruent to angle A	5. Base angles of an isosceles triangle are congruent
6. angle A is congruent to angle D	6. (Definition of angle congruency?)

 

[srmichael]

I forgot that I'd posted this ages ago..... I came across it again as I was getting my papers in order to send off to my teacher




After the parts of my proof that I already submitted I have:

4. angle C is congruent to angle D	4. Base angles of an isosceles triangle are congruent
5. angle C is congruent to angle A	5. Base angles of an isosceles triangle are congruent
6. angle A is congruent to angle D	6. (Definition of angle congruency?)

How 'bout transitive property (If a = b and b=c, then a=c) or in your case, if D = C and C = A, then D = A.

 

[Mrspi]

How 'bout transitive property (If a = b and b=c, then a=c) or in your case, if D = C and C = A, then D = A.

When two or more angles have the SAME vertex, then one cannot simply refer to the angle by its vertex. You have used the name "< C"....but there are two distinct angles with C as the vertex, and I'm pretty sure you don't mean the SAME angle. Since when you say <A = <C and <D = <C, the "<C" used in one statement is not the same angle as the "<C" in the other statement...thus, you can't use the transitive property to state that <A = <D.

You need to use three-letter names for the two different angles at C. And they are vertical angles, so those angles are congruent by the theorem which states "Vertical angles are congruent."

I see that you DID that in your first attempt at the proof...GOOD! Now, combine that with the statements about the base angles of an isosceles triangle. Use the correct three-letter name for the angle at C you are referring to in each statement.

 

[vampirewitchreine]

How 'bout transitive property (If a = b and b=c, then a=c) or in your case, if D = C and C = A, then D = A.

When two or more angles have the SAME vertex, then one cannot simply refer to the angle by its vertex. You have used the name "< C"....but there are two distinct angles with C as the vertex, and I'm pretty sure you don't mean the SAME angle. Since when you say <A = <C and <D = <C, the "<C" used in one statement is not the same angle as the "<C" in the other statement...thus, you can't use the transitive property to state that <A = <D.

You need to use three-letter names for the two different angles at C. And they are vertical angles, so those angles are congruent by the theorem which states "Vertical angles are congruent."

I see that you DID that in your first attempt at the proof...GOOD! Now, combine that with the statements about the base angles of an isosceles triangle. Use the correct three-letter name for the angle at C you are referring to in each statement.

So I should change statements 4 and 5 to say:
4. angle BAC is congruent to angle BCA and 5. angle EDC is congruent to angle ECD? Correct?


Should I also take my statement 2 and move it down to under the statements that I just corrected and then be able to get angle A is congruent to angle D? Making my proof:

Statement	Reason
1. segment AB is congruent to segment BC	1. Given
2. segment DE is congruent to segment EC	2. Given
3. angle BAC is congruent to angle BCA	3. Base angles of an isosceles triangle are congruent
4. angle ECD is congruent to angle EDC	4. Base angles of an isosceles triangle are congruent
5. angle ECD is congruent to angle BCA	5. Vertical angles are congruent
6. angle A is congruent to angle D	6. ?????

(6 has to remain as the one letter because that's all that my book asked for)

 

[Mrspi]

So I should change statements 4 and 5 to say:
4. angle BAC is congruent to angle BCA and 5. angle EDC is congruent to angle ECD? Correct?


Should I also take my statement 2 and move it down to under the statements that I just corrected and then be able to get angle A is congruent to angle D? Making my proof:

Statement	Reason
1. segment AB is congruent to segment BC	1. Given
2. segment DE is congruent to segment EC	2. Given
3. angle BAC is congruent to angle BCA angle A is congruent to angle BCA	3. Base angles of an isosceles triangle are congruent
4. angle ECD is congruent to angle EDC angle ECD is congruent to angle D	4. Base angles of an isosceles triangle are congruent
5. angle ECD is congruent to angle BCA	5. Vertical angles are congruent
6. angle A is congruent to angle D	6. ????? If two angles are congruent to the same or congruent angles, they are congruent to each other.

(6 has to remain as the one letter because that's all that my book asked for)

See my suggestions in blue.

 

[vampirewitchreine]

Thank you. It makes so much more sense with having A and D congruent to the vertical angles and then proving them congruent (I seem to always make these more complicated than they really are for some reason.)