Question

complete the two - column proof. given: a||b prove: ∠2≅∠7 statements reasons 1. a||b 1. given 2. m∠6 + m∠7 = 180 2. __ 3. m∠6 + m∠2 = 180 3. __ 4. m∠6 + m∠2 = m∠6 + m∠7 4. transitive property of equality 5. m∠2 = m∠7 5. subtraction property of equality 6. ∠2≅∠7 6. definition of congruent angles a 2. linear pair postulate 3. same - side exterior angles postulate b 2. same - side interior angles postulate 3. linear pair postulate c 2. linear pair postulate 3. linear pair postulate d 2. linear pair postulate 3. same - side interior angles postulate question 14(1 point) the map given shows the relationship between three streets. suppose that m∠1 + m∠2 = 180°. are maple street and elm street parallel? explain. question 15(1 point) what is the relationship between ∠4 and ∠5? a alternate exterior angles b alternate interior angles c same - side interior angles d corresponding angles

Explanation:

Question 13:

Step1: Analyze statement 2

Since $\angle6$ and $\angle7$ form a linear - pair (adjacent angles that form a straight - line), by the Linear Pair Postulate, the sum of their measures is 180. So the reason for statement 2 is Linear Pair Postulate.

Step2: Analyze statement 3

$\angle6$ and $\angle2$ are same - side interior angles. When $a\parallel b$, by the Same - Side Interior Angles Postulate, the sum of same - side interior angles is 180. So the reason for statement 3 is Same - Side Interior Angles Postulate.

Question 14:

Step1: Recall parallel line postulates

If the sum of same - side interior angles formed by two lines and a transversal is 180, then the two lines are parallel. Here, $\angle1$ and $\angle2$ are same - side interior angles formed by Maple Street, Elm Street and River Drive (the transversal), and $m\angle1 + m\angle2=180^{\circ}$.

Step2: Conclusion

So, Maple Street and Elm Street are parallel because the sum of same - side interior angles is 180.

Question 15:

Step1: Identify angle relationship

$\angle4$ and $\angle5$ are alternate interior angles. Alternate interior angles are non - adjacent angles that lie between two lines and on opposite sides of a transversal. Here, lines $m$ and $n$ are the two lines and the transversal intersects them, and $\angle4$ and $\angle5$ are between $m$ and $n$ and on opposite sides of the transversal.

Answer:

Question 13: d
Question 14: Yes, because the sum of same - side interior angles ($\angle1$ and $\angle2$) is 180.
Question 15: b. alternate interior angles