given: $ \triangle def \cong \triangle gfe; \angle 3 \cong \angle 7 $ prove: $ \triangle dhe \cong \triangle ghf $ complete the statements in the two - column proof. enter your answers in the boxes.

| statements | reasons |
| --- | --- |
| 1. $ \triangle def \cong \triangle gfe $ | 1. given |
| 2. $ \overline{de} \cong \overline{gf} $ | 2. cpctc |
| 3. $ \angle 3 \cong \angle 7 $ | 3. given |
| 4. $ \angle \square \cong \angle \square $ | 4. vertical angles theorem |
| 5. $ \triangle dhe \cong \triangle ghf $ | 5. aas |

Question

given: $ \triangle def \cong \triangle gfe; \angle 3 \cong \angle 7 $ prove: $ \triangle dhe \cong \triangle ghf $ complete the statements in the two - column proof. enter your answers in the boxes.

| statements | reasons |
| --- | --- |
| 1. $ \triangle def \cong \triangle gfe $ | 1. given |
| 2. $ \overline{de} \cong \overline{gf} $ | 2. cpctc |
| 3. $ \angle 3 \cong \angle 7 $ | 3. given |
| 4. $ \angle \square \cong \angle \square $ | 4. vertical angles theorem |
| 5. $ \triangle dhe \cong \triangle ghf $ | 5. aas |

Accepted Answer

# Explanation:
## Step1: Recall vertical angles
Vertical angles are formed when two lines intersect. In the given figure, $\angle DHE$ and $\angle GHF$ are vertical angles.

## Step2: Use vertical angles theorem
The vertical angles theorem states that vertical angles are congruent. So, $\angle DHE\cong\angle GHF$

# Answer:
$\angle DHE\cong\angle GHF$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall vertical angles

Step2: Use vertical angles theorem

Answer:

statements	reasons
2. \\( \overline{de} \cong \overline{gf} \\)	2. cpctc
3. \\( \angle 3 \cong \angle 7 \\)	3. given
4. \\( \angle \square \cong \angle \square \\)	4. vertical angles theorem
5. \\( \triangle dhe \cong \triangle ghf \\)	5. aas