Question

Given: ∠1≅∠2, DH¯¯¯¯¯¯¯¯¯
bisects ∠BDF


Prove: ΔBDH ≅ ΔFDH



(5 points)
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Statement Reason

1. DH¯¯¯¯¯¯¯¯¯
bisects ∠BDF
1.

2. ∠BDH≅∠FDH
2.

3. HD¯¯¯¯¯¯¯¯¯≅HD¯¯¯¯¯¯¯¯¯
3.

4. ∠1≅∠2
4.

5. △DAB≅△BCD
5. Response area

Answer 1

To prove that ΔBDH ≅ ΔFDH using the information given, we can fill in the statements and reasons as follows:

| Statement | Reason |
|-----------------------------------------------|------------------------------------------|
| 1. DH bisects ∠BDF | 1. Given |
| 2. ∠BDH ≅ ∠FDH | 2. Angle Bisector Theorem |
| 3. HD ≅ HD | 3. Reflexive Property of Congruence |
| 4. ∠1 ≅ ∠2 | 4. Given (since DH bisects ∠BDF) |
| 5. ΔBDH ≅ ΔFDH | 5. Angle-Side-Angle (ASA) Postulate |

This arrangement clearly outlines the statements and their corresponding reasons leading to the conclusion that ΔBDH is congruent to ΔFDH.