Given: ∠1 ≅ ∠2;

Question

Prove: ∠3 ≅ ∠4

(6 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. ∠1 ≅ ∠2 1. Response area
2. 2. Response area
3. WP¯¯¯¯¯¯¯¯¯≅ZP¯¯¯¯¯¯¯
3. Response area
4. △WXP≅△ZYP
4. Response area
5. XP¯¯¯¯¯¯¯¯≅YP¯¯¯¯¯¯¯¯
5. Response area
6. ∠3 ≅ ∠4 6. Response area

Answer 1

Here are the completed statements and reasons to prove that ∠3 ≅ ∠4 given that ∠1 ≅ ∠2:

| Statement | Reason | |---------------------------------------------|-----------------------------------| | 1. ∠1 ≅ ∠2 | 1. Given | | 2. WP¯¯¯¯¯¯¯¯¯≅ZP¯¯¯¯¯¯¯ | 2. Corresponding Parts of Congruent Triangles are Congruent (CPCTC) | | 3. △WXP≅△ZYP | 3. Angle-Angle-Angle (AAA) Congruence | | 4. XP¯¯¯¯¯¯¯¯≅YP¯¯¯¯¯¯¯¯¯ | 4. CPCTC | | 5. ∠3 ≅ ∠4 | 5. CPCTC |

Completed Table:

| Statement | Reason | |---------------------------------------------|-----------------------------------| | 1. ∠1 ≅ ∠2 | 1. Given | | 2. WP¯¯¯¯¯¯¯¯¯≅ZP¯¯¯¯¯¯¯ | 2. CPCTC | | 3. △WXP≅△ZYP | 3. Angle-Angle-Angle (AAA) Congruence | | 4. XP¯¯¯¯¯¯¯¯≅YP¯¯¯¯¯¯¯¯¯ | 4. CPCTC | | 5. ∠3 ≅ ∠4 | 5. CPCTC |

This proof shows that since we have congruent angles, we can conclude that the corresponding angles (∠3 and ∠4) are also congruent. Make sure to adjust the specific congruence property mentioned, such as AAA or whichever applicable based on the specifics of your diagram.