Questions: Finish the triangle proof by dragging the correct reasons to their box. There will be two extra unused reasons! Given: D is the midpoint of AF, D is the midpoint of EC Prove: triangle EDF is congruent to triangle CDA Statement Reason ------ D is the midpoint of AF D is the midpoint of EC ED is congruent to CD FD is congruent to AD angle EDF is congruent to angle CDA triangle EDF is congruent to triangle CDA Vertical Angles Definition of Midpoint Reflexive Property Given Definition of Midpoint ASA SAS

Finish the triangle proof by dragging the correct reasons to their box. There will be two extra unused reasons!

Given: D is the midpoint of AF, D is the midpoint of EC
Prove: triangle EDF is congruent to triangle CDA

 Statement  Reason 
------
 D is the midpoint of AF  
 D is the midpoint of EC  
 ED is congruent to CD  
 FD is congruent to AD  
 angle EDF is congruent to angle CDA  
 triangle EDF is congruent to triangle CDA  

Vertical Angles
Definition of Midpoint
Reflexive Property
Given
Definition of Midpoint
ASA
SAS
Transcript text: Finish the triangle proof by dragging the correct reasons to their box. There will be two extra unused reasons! Given: $D$ is the midpoint of $AF$, $D$ is the midpoint of $EC$ Prove: $\triangle \mathrm{EDF} \cong \triangle \mathrm{CDA}$ \begin{tabular}{|l|l|l|l|} \hline & \multicolumn{1}{|c|}{ Statement } & & \multicolumn{1}{c|}{ Reason } \\ \hline 1. & \begin{tabular}{l} D is the \\ midpoint of $AF$ \end{tabular} & 1. & \\ \hline 2. & \begin{tabular}{l} D is the \\ midpoint of $EC$ \end{tabular} & 2. & \\ \hline 3. & $ED \cong CD$ & 3. & \\ \hline 4. & $FD \cong AD$ & 4. & \\ \hline 5. & $\angle EDF \cong \angle CDA$ & 5. & \\ \hline 6. & $\triangle EDF \cong \triangle CDA$ & 6. & \\ \hline \end{tabular} Vertical Angles Definition of Midpoint Reflexive Property Given Definition of Midpoint ASA SAS
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Solution

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Solution Steps

Step 1: Reason for statements 1 and 2

Statements 1 and 2, "D is the midpoint of AF" and "D is the midpoint of EC", are given in the problem.

Step 2: Reason for statements 3 and 4

Statements 3 and 4, "ED ≅ CD" and "FD ≅ AD", follow from the definition of a midpoint. Since D is the midpoint of EC, ED and CD are congruent. Similarly, since D is the midpoint of AF, FD and AD are congruent.

Step 3: Reason for statement 5

Statement 5, "∠EDF ≅ ∠CDA", is true because the angles are vertical angles.

Step 4: Reason for statement 6

Statement 6, "ΔEDF ≅ ΔCDA", follows from the Side-Angle-Side (SAS) congruence postulate. We have two pairs of congruent sides (ED ≅ CD and FD ≅ AD) and the included angles are congruent (∠EDF ≅ ∠CDA).

Final Answer

| & Statement & & Reason \\ |---|---|---|---| | 1. | D is the midpoint of AF | 1. | Given \\ | 2. | D is the midpoint of EC | 2. | Given \\ | 3. | ED ≅ CD | 3. | Definition of Midpoint \\ | 4. | FD ≅ AD | 4. | Definition of Midpoint \\ | 5. | ∠EDF ≅ ∠CDA | 5. | Vertical Angles are Congruent \\ | 6. | ΔEDF ≅ ΔCDA | 6. | SAS Congruence Postulate \\

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