Question

Question

Complete the proof by filling in the blanks for A - F. (If you would like to write it on paper, you may take a picture of your work and submit it)

Statement Reason
1. AB¯¯¯¯¯¯¯¯≅CB¯¯¯¯¯¯¯¯
1. ___A___
2. ___B___ 2. Given
3. ___C___ 3. ___D___
4. △ABD≅
___E___ 4. ___F___


(6 points)

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page 17 of 17

Answer 1

To complete the proof, we need to fill in the blanks logically based on the given statements and basic geometry principles. Here’s a possible completion of the proof:

Statement | Reason --- | ---

1. \( AB \cong CB \) | 1. Given

2.  \\( AD \cong CD \\)	| 2.  **Given**
   

3.  \\( BD \cong BD \\)	| 3.  **Reflexive Property of Congruence**
   

4. \( \triangle ABD \cong \triangle CBD \) | 4. Side-Side-Side (SSS) Congruence Postulate

So to summarize:

• A: Given
• B: \( AD \cong CD \)
• C: \( BD \cong BD \)
• D: Reflexive Property of Congruence
• E: \( CBD \)
• F: Side-Side-Side (SSS) Congruence Postulate

This proof shows that Triangle ABD is congruent to Triangle CBD by demonstrating the three sides of both triangles are congruent through the SSS postulate.