Questions: Finish the triangle proof by dragging the correct reasons to their box. There will be two extra unused reasons! Given: AB∣ ED, C is the midpoint of BE Prove: triangle ABC ≅ triangle DEC - Statement Reason - AB∣ ED - C is the midpoint of BE - angle ABC ≅ angle DEC - BC ≅ EC - angle ACB ≅ angle DCE - triangle ABC ≅ triangle DEC

Finish the triangle proof by dragging the correct reasons to their box. There will be two extra unused reasons!
Given: AB∣ ED, C is the midpoint of BE
Prove: triangle ABC ≅ triangle DEC

- Statement Reason
- AB∣ ED
- C is the midpoint of BE
- angle ABC ≅ angle DEC
- BC ≅ EC
- angle ACB ≅ angle DCE
- triangle ABC ≅ triangle DEC

Transcript text: Finish the triangle proof by dragging the correct reasons to their box. There will be two extra unused reasons! Given: $\mathrm{AB}|\mid ED, C$ is the midpoint of $BE$ Prove: $\triangle ABC \cong \triangle DEC$ \begin{tabular}{|l|l|l|l|} \hline & \multicolumn{1}{|c|}{ Statement } & & \multicolumn{1}{c|}{ Reason } \\ \hline 1. & $AB|\mid ED$ & 1. & \\ \hline 2. & \begin{tabular}{l} $C$ is the \\ midpoint of $BE$ \end{tabular} & 2. & \\ \hline 3. & $\angle ABC \cong \angle DEC$ & 3. & \\ \hline 4. & $BC \cong EC$ & 4. & \\ \hline 5. & $\angle ACB \cong \angle DCE$ & 5. & \\ \hline 6. & $\triangle ABC \cong \triangle DEC$ & 6. & \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Reason for statement 1

The first statement, $AB \parallel ED$, is given.

Step 2: Reason for statement 2

The second statement, C is the midpoint of BE, is also given.

Step 3: Reason for statement 3

Since $AB \parallel ED$, we know that $\angle ABC$ and $\angle DEC$ are alternate interior angles. Therefore, they are congruent. The reason is: Alternate Interior Angles Theorem.

Step 4: Reason for statement 4

Since C is the midpoint of BE, BC and EC are congruent. The reason is: Definition of Midpoint.

Step 5: Reason for statement 5

$\angle ACB$ and $\angle DCE$ are vertical angles, thus they are congruent. The reason is: Vertical Angles Theorem.

Step 6: Reason for statement 6

We have shown that two angles ($\angle ABC \cong \angle DEC$ and $\angle ACB \cong \angle DCE$) and the included side ($BC \cong EC$) of $\triangle ABC$ are congruent to the corresponding two angles and included side of $\triangle DEC$. Therefore, the triangles are congruent by the Angle-Side-Angle (ASA) Congruence Postulate.