2 of 32 of 3 Items

Question

2 of 32 of 3 Items

Question
Prove that the triangles are congruent.

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

Prove: ΔBDH ≅ ΔFDH

(5 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Statement                                                       Reason

1.  DH¯¯¯¯¯¯¯¯¯
    bisects ∠BDF
                           1.  Response area

2.  ∠BDH≅∠FDH
                                    2.  Response area

3.  HD¯¯¯¯¯¯¯¯¯≅HD¯¯¯¯¯¯¯¯¯
                                              3.  Response area

4.  ∠1≅∠2
                                                 4.  Response area

5.  △DAB≅△BCD
                                  5.  Response area

Skip

GPT-4o mini · Answer

To prove that triangles $ \Delta BDH $ and $ \Delta FDH $ are congruent, we can use the information given. Here's how the proof can be structured with the relevant statements and reasons: | Statement | Reason | |-----------------------------------------------------|------------------------------------------------------| | 1. $ DH $ bisects $ \angle BDF $ | Given | | 2. $ \angle BDH \cong \angle FDH $ | Definition of angle bisector | | 3. $ HD \cong HD $ | Reflexive property of congruence | | 4. $ \angle 1 \cong \angle 2 $ | Given | | 5. $ \Delta BDH \cong \Delta FDH $ | Angle-Side-Angle (ASA) congruence criterion | **Note**: The specific references to angles could be adjusted if $ \angle 1 $ and $ \angle 2 $ are associated with $ \angle BDH $ and $ \angle FDH $ respectively. Also, make sure to clarify that angles $ \angle 1 $ and $ \angle 2 $ correspond to $ \angle BDH $ and $ \angle FDH $. As such, here is the adjusted table with the correct references if necessary: | Statement | Reason | |-----------------------------------------------------|------------------------------------------------------| | 1. $ DH $ bisects $ \angle BDF $ | Given | | 2. $ \angle BDH \cong \angle FDH $ | Definition of angle bisector | | 3. $ HD \cong HD $ | Reflexive property of congruence | | 4. $ \angle 1 \cong \angle 2 $ | Given | | 5. $ \Delta BDH \cong \Delta FDH $ | Angle-Side-Angle (ASA) congruence criterion | By stating these sequentially, we demonstrate that the triangles are congruent based on the given information and properties of congruence.