given $ \triangle d e f $ and $ \overleftrightarrow{e g} \| \overline{d f} $, complete the proof that $ m \angle 1+m \angle 2+m \angle 3=180^{circ} $.

select and drag tiles to the empty boxes to complete the proof correctly.

| statement | reason |
| --- | --- |
| 1. $ \overrightarrow{e g} \| \overline{d f} $ | 1. given |
| 2. | 2. when parallel lines are cut by a transversal, alternate interior angles are congruent. |
| 3. $ m \angle 4+m \angle 2+m \angle 5=180^{circ} $ | 3. the measure of angles that complete a line sum to $ 180^{circ} $. |
| 4. $ m \angle 1+m \angle 2+m \angle 3=180^{circ} $ | 4. |

$ \angle 1 \cong \angle 4 $ and $ \angle 2 \cong \angle 3 $ $ \angle 1 \cong \angle 4 $ and $ \angle 3 \cong \angle 5 $ substitution property of equality addition property of equality

Question

given $ \triangle d e f $ and $ \overleftrightarrow{e g} \| \overline{d f} $, complete the proof that $ m \angle 1+m \angle 2+m \angle 3=180^{circ} $.

select and drag tiles to the empty boxes to complete the proof correctly.

| statement | reason |
| --- | --- |
| 1. $ \overrightarrow{e g} \| \overline{d f} $ | 1. given |
| 2. | 2. when parallel lines are cut by a transversal, alternate interior angles are congruent. |
| 3. $ m \angle 4+m \angle 2+m \angle 5=180^{circ} $ | 3. the measure of angles that complete a line sum to $ 180^{circ} $. |
| 4. $ m \angle 1+m \angle 2+m \angle 3=180^{circ} $ | 4. |

$ \angle 1 \cong \angle 4 $ and $ \angle 2 \cong \angle 3 $ $ \angle 1 \cong \angle 4 $ and $ \angle 3 \cong \angle 5 $ substitution property of equality addition property of equality

Accepted Answer

# Explanation:
## Step1: Identify congruent angles
Since $ \overleftrightarrow{EG}\parallel\overleftrightarrow{DF}$, when parallel lines are cut by a transversal:
- $ \angle1$ and $ \angle4$ are alternate - interior angles ($ \angle1\cong\angle4$).
- $ \angle3$ and $ \angle5$ are alternate - interior angles ($ \angle3\cong\angle5$).
So, the statement for step 2 is $ \angle1\cong\angle4$ and $ \angle3\cong\angle5$.
## Step2: Justify the final equality
We know that $ m\angle4 + m\angle2 + m\angle5=180^{\circ}$ (from step 3).
By the substitution property of equality, if $ \angle1\cong\angle4$ (so $ m\angle1 = m\angle4$) and $ \angle3\cong\angle5$ (so $ m\angle3 = m\angle5$), we can substitute $ m\angle4$ with $ m\angle1$ and $ m\angle5$ with $ m\angle3$ in the equation $ m\angle4 + m\angle2 + m\angle5 = 180^{\circ}$.

# Answer:
2. $ \angle1\cong\angle4$ and $ \angle3\cong\angle5$
4. Substitution Property of Equality

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Identify congruent angles

Step2: Justify the final equality

Answer:

statement	reason
2.	2. when parallel lines are cut by a transversal, alternate interior angles are congruent.
3. \\( m \angle 4+m \angle 2+m \angle 5=180^{circ} \\)	3. the measure of angles that complete a line sum to \\( 180^{circ} \\).
4. \\( m \angle 1+m \angle 2+m \angle 3=180^{circ} \\)	4.