Question

1. use the diagram below to decide if the following statements are true or false. choose one justification from the list to justify your response.

a. linear pairs are supplementary
b. vertical angles are congruent
c. corresponding angles are congruent when they are formed by parallel lines
d. alternate interior angles are congruent when they are formed by parallel lines
e. same side interior angles are supplementary when they are formed by parallel lines
f. alternate exterior angles are congruent when they are formed by parallel lines
g. the statement is false

statement

justification

a) |∠4≅∠6|
b) |∠1≅∠8|
c) |∠1 and ∠5 are supplementary|
d) |∠2≅∠3|
e) |∠7 and ∠8 are supplementary|
f) |∠8≅∠4|

Explanation:

Step1: Identify angle - pair relationships

• $\angle4$ and $\angle6$ are alternate interior angles. Since the lines are parallel, by the property that alternate interior angles formed by parallel lines are congruent, $\angle4\cong\angle6$. Justification: d. Alternate interior angles are congruent when they are formed by parallel lines.

Step2: Analyze $\angle1$ and $\angle8$

• $\angle1$ and $\angle8$ are alternate exterior angles. For parallel lines, alternate exterior angles are congruent. Justification: f. Alternate exterior angles are congruent when they are formed by parallel lines.

Step3: Examine $\angle1$ and $\angle5$

• $\angle1$ and $\angle5$ are corresponding angles. Corresponding angles formed by parallel lines are congruent, not supplementary. Justification: g. The statement is false.

Step4: Look at $\angle2$ and $\angle3$

• $\angle2$ and $\angle3$ are vertical angles. Vertical angles are congruent. Justification: b. Vertical angles are congruent.

Step5: Analyze $\angle7$ and $\angle8$

• $\angle7$ and $\angle8$ are a linear - pair. Linear pairs are supplementary. Justification: a. Linear pairs are supplementary.

Step6: Examine $\angle8$ and $\angle4$

• $\angle8$ and $\angle4$ are corresponding angles. Since the lines are parallel, corresponding angles are congruent. Justification: c. Corresponding angles are congruent when they are formed by parallel lines.

Answer:

a) Justification: d. Alternate interior angles are congruent when they are formed by parallel lines
b) Justification: f. Alternate exterior angles are congruent when they are formed by parallel lines
c) Justification: g. The statement is false
d) Justification: b. Vertical angles are congruent
e) Justification: a. Linear pairs are supplementary
f) Justification: c. Corresponding angles are congruent when they are formed by parallel lines