2 - 1 additional practice
parallel lines
use the figure for exercises 1 - 4. identify all pairs of each type of angle.
1. corresponding angles
2. same - side interior angles
3. alternate exterior angles
4. alternate interior angles
use the figure for exercises 5 and 6.
5. which angles are supplementary to the given angle?
6. which angles are congruent to the given angle?
7. complete the two - column proof.
given: ( xparallel y )
prove: ( angle3congangle5 )

| statements | reasons |
| --- | --- |
| 1) ( xparallel y ) | 1) given |
| 2) ( mangle3 + mangle8=180^{circ} ) | 2) same side |
| 3) ( mangle5 + mangle8 = 180^{circ} ) | 3) substitute |
| 4) | 4) transitive property of equality |
| 5) | 5) subtraction property of equality |
| 6) | 6) definition of congruence |

Question

2 - 1 additional practice
parallel lines
use the figure for exercises 1 - 4. identify all pairs of each type of angle.
1. corresponding angles
2. same - side interior angles
3. alternate exterior angles
4. alternate interior angles
use the figure for exercises 5 and 6.
5. which angles are supplementary to the given angle?
6. which angles are congruent to the given angle?
7. complete the two - column proof.
given: ( xparallel y )
prove: ( angle3congangle5 )

| statements | reasons |
| --- | --- |
| 1) ( xparallel y ) | 1) given |
| 2) ( mangle3 + mangle8=180^{circ} ) | 2) same side |
| 3) ( mangle5 + mangle8 = 180^{circ} ) | 3) substitute |
| 4) | 4) transitive property of equality |
| 5) | 5) subtraction property of equality |
| 6) | 6) definition of congruence |

Accepted Answer

# Explanation:
## Step1: Identify the reason for statement 2
When two parallel lines are cut by a transversal, same - side interior angles are supplementary. So, the reason for $m\angle3 + m\angle8=180^{\circ}$ is "Same - side interior angles theorem".
## Step2: Identify the reason for statement 3
$\angle5$ and $\angle8$ are adjacent angles that form a linear pair. By the linear - pair postulate, $m\angle5 + m\angle8 = 180^{\circ}$.
## Step3: Write statement 4
Since $m\angle3 + m\angle8=180^{\circ}$ and $m\angle5 + m\angle8 = 180^{\circ}$, by the transitive property of equality, $m\angle3 + m\angle8=m\angle5 + m\angle8$.
## Step4: Write statement 5
Subtract $m\angle8$ from both sides of the equation $m\angle3 + m\angle8=m\angle5 + m\angle8$. Using the subtraction property of equality, we get $m\angle3=m\angle5$.
## Step5: Write statement 6
If $m\angle3=m\angle5$, then by the definition of congruent angles ($\angle A\cong\angle B$ if and only if $m\angle A = m\angle B$), $\angle3\cong\angle5$.

# Answer:
| Statements | Reasons |
|---|---|
| 1) $x\parallel y$ | 1) Given |
| 2) $m\angle3 + m\angle8 = 180^{\circ}$ | 2) Same - side interior angles theorem |
| 3) $m\angle5 + m\angle8 = 180^{\circ}$ | 3) Linear - pair postulate |
| 4) $m\angle3 + m\angle8=m\angle5 + m\angle8$ | 4) Transitive Property of Equality |
| 5) $m\angle3=m\angle5$ | 5) Subtraction Property of Equality |
| 6) $\angle3\cong\angle5$ | 6) Definition of congruence |

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Identify the reason for statement 2

Step2: Identify the reason for statement 3

Step3: Write statement 4

Step4: Write statement 5

Step5: Write statement 6

Answer:

statements	reasons
2) ( mangle3 + mangle8=180^{circ} )	2) same side
3) ( mangle5 + mangle8 = 180^{circ} )	3) substitute
4)	4) transitive property of equality
5)	5) subtraction property of equality
6)	6) definition of congruence

Statements	Reasons
2) \(m\angle3 + m\angle8 = 180^{\circ}\)	2) Same - side interior angles theorem
3) \(m\angle5 + m\angle8 = 180^{\circ}\)	3) Linear - pair postulate
4) \(m\angle3 + m\angle8=m\angle5 + m\angle8\)	4) Transitive Property of Equality
5) \(m\angle3=m\angle5\)	5) Subtraction Property of Equality
6) \(\angle3\cong\angle5\)	6) Definition of congruence