I need some help with this proof. This is the image link: h t t p s : / / p a s t e b o a r d . c o / H X I F 4 FJ . p n g
The given is : C is the intersection point of segment AD and Segment EB. Segment AC and EC are congruent and <A and <E are also congruent.
Write a two column proof proving that segment AB is congruent to segment ED.
I have the given but I am not sure where to go from there. Can you help me please?
angles ACB and ECD are congruent, since they are vertical angles.
Therefore, triangles ACB and ECD are congruent, by ASA
AB is congruent to ED by CPCTC
Thank you so Much!
Of course, I can help you with the proof!
To prove that segment AB is congruent to segment ED, we can use a combination of congruent triangles and the transitive property.
Here's how you can set up your two-column proof:
Statement | Reason
--------------------------------------------------------------------|----------
1. C is the intersection point of segment AD and segment EB | Given
2. AC is congruent to EC | Given
3. <A is congruent to <E | Given
4. Draw segment CB and segment DA | Construction
5. Triangle ACB is congruent to triangle ECB | SAS (Side-Angle-Side) congruence postulate
6. AB is congruent to EB | CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
7. Triangle EDA is congruent to triangle BDA | ASA (Angle-Side-Angle) congruence postulate
8. ED is congruent to AD | CPCTC
9. AB is congruent to ED | Transitive Property of Congruence
Let me go over the steps:
1. The given information states that point C is the intersection point of segment AD and segment EB.
2. Given that segment AC and segment EC are congruent.
3. Given that angle A and angle E are congruent.
4. Draw segment CB and segment DA to create triangles ACB and ECB for the congruence statement.
5. Using the SAS congruence postulate, we can conclude that triangle ACB is congruent to triangle ECB.
6. Since the corresponding parts of congruent triangles are congruent (CPCTC), we can conclude that segment AB is congruent to segment EB.
7. Draw segment DA to create triangles EDA and BDA for the congruence statement.
8. Using the ASA congruence postulate, we can conclude that triangle EDA is congruent to triangle BDA.
9. Applying CPCTC again, we can conclude that segment ED is congruent to segment AD.
10. Finally, using the transitive property of congruence, we can conclude that segment AB is congruent to segment ED.
I hope this helps! Let me know if you have any further questions.