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

Here's how to complete the proof for the congruence of triangles \( \triangle BDH \) and \( \triangle FDH \):

| Statement | Reason |
|-------------------------------------------|-------------------------------------------|
| 1. \( DH \) bisects \( \angle BDF \) | 1. Given |
| 2. \( \angle BDH \cong \angle FDH \) | 2. Definition of angle bisector |
| 3. \( HD \cong HD \) | 3. Reflexive property of congruence |
| 4. \( \angle 1 \cong \angle 2 \) | 4. Given (as \( \angle BDH \) and \( \angle FDH \) are the angles formed by bisector) |
| 5. \( \triangle BDH \cong \triangle FDH \) | 5. Angle-Side-Angle (ASA) Congruence Postulate |

You can fill in the responses to match the statements and reasons accordingly.