Write a two column proof. Given CE = CA, EB and AD are medians, Prove: EB = AD for a triangle
To write a two-column proof, we will list each statement in the left column, and the corresponding reason or justification in the right column. Here's how you can prove that EB = AD for a triangle using given information:
Statement Reason
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1. CE = CA Given
2. EB is a median Definition of median
3. AD is a median Definition of median
4. CE = AE Definition of median
5. EB = AE Substitution (Statement 1 and 4)
6. AD = AE Substitution (Statement 1)
7. EB = AD Transitive property (Statement 5 and 6)
In this proof, we start with the given statement that CE = CA. Then we use the definition of medians to state that EB and AD are medians. Since both EB and AD pass through the vertex A, they both divide the opposite side into two equal segments.
Next, we state that CE = AE because both segments are equal due to the median property. Using this information, we can substitute CE = AE into the previous equation EB = AE, giving us EB = AD. Finally, we conclude that EB = AD using the transitive property, which states that if two quantities are equal to a third quantity, then they are equal to each other.