Question

for questions 9 - 11, find the values of x and y if l || m.

1. 10x - 17 = 6x + 11, 4y+24 + 73 = 180
2. 7x - 30 = 5x + 14, 124 + 3y+11 = 180
3. 23y - 16+6y - 21 = 180

topic: proving lines are parallel

1. given the following information, determine which lines, if any, are parallel. state the converse that justifies your answer.

given\tparallel lines\tconverse
a. ∠8≅∠20
b. ∠1≅∠9
c. m∠3 + m∠10 = 180°
d. ∠11≅∠16
e. m∠6 + m∠24 = 180°
f. ∠14≅∠23
g. ∠4≅∠21
h. m∠8 + m∠18 = 180°
i. ∠5≅∠15

Explanation:

Step1: Recall parallel - line angle relationships

When two lines are parallel, corresponding angles are congruent, alternate - interior angles are congruent, and same - side interior angles are supplementary.

Step2: Analyze each given angle relationship

a. $\angle8\cong\angle20$

These are corresponding angles. If $\angle8\cong\angle20$, then the lines that the transversal intersects are parallel. The converse is the Corresponding Angles Converse. Parallel Lines: The lines that $\angle8$ and $\angle20$ are formed on are parallel.

b. $\angle1\cong\angle9$

These are corresponding angles. If $\angle1\cong\angle9$, then the lines are parallel by the Corresponding Angles Converse. Parallel Lines: The lines that $\angle1$ and $\angle9$ are formed on are parallel.

c. $m\angle3 + m\angle10=180^{\circ}$

These are same - side interior angles. If $m\angle3 + m\angle10 = 180^{\circ}$, then the lines are parallel by the Same - Side Interior Angles Converse. Parallel Lines: The lines that $\angle3$ and $\angle10$ are formed on are parallel.

d. $\angle11\cong\angle16$

These are alternate interior angles. If $\angle11\cong\angle16$, then the lines are parallel by the Alternate Interior Angles Converse. Parallel Lines: The lines that $\angle11$ and $\angle16$ are formed on are parallel.

e. $m\angle6 + m\angle24=180^{\circ}$

These are same - side interior angles. If $m\angle6 + m\angle24 = 180^{\circ}$, then the lines are parallel by the Same - Side Interior Angles Converse. Parallel Lines: The lines that $\angle6$ and $\angle24$ are formed on are parallel.

f. $\angle14\cong\angle23$

These are alternate interior angles. If $\angle14\cong\angle23$, then the lines are parallel by the Alternate Interior Angles Converse. Parallel Lines: The lines that $\angle14$ and $\angle23$ are formed on are parallel.

g. $\angle4\cong\angle21$

These are corresponding angles. If $\angle4\cong\angle21$, then the lines are parallel by the Corresponding Angles Converse. Parallel Lines: The lines that $\angle4$ and $\angle21$ are formed on are parallel.

h. $m\angle8 + m\angle18=180^{\circ}$

These are same - side interior angles. If $m\angle8 + m\angle18 = 180^{\circ}$, then the lines are parallel by the Same - Side Interior Angles Converse. Parallel Lines: The lines that $\angle8$ and $\angle18$ are formed on are parallel.

i. $\angle5\cong\angle15$

These are corresponding angles. If $\angle5\cong\angle15$, then the lines are parallel by the Corresponding Angles Converse. Parallel Lines: The lines that $\angle5$ and $\angle15$ are formed on are parallel.

Answer:

a. Parallel Lines: The lines that $\angle8$ and $\angle20$ are formed on; Converse: Corresponding Angles Converse
b. Parallel Lines: The lines that $\angle1$ and $\angle9$ are formed on; Converse: Corresponding Angles Converse
c. Parallel Lines: The lines that $\angle3$ and $\angle10$ are formed on; Converse: Same - Side Interior Angles Converse
d. Parallel Lines: The lines that $\angle11$ and $\angle16$ are formed on; Converse: Alternate Interior Angles Converse
e. Parallel Lines: The lines that $\angle6$ and $\angle24$ are formed on; Converse: Same - Side Interior Angles Converse
f. Parallel Lines: The lines that $\angle14$ and $\angle23$ are formed on; Converse: Alternate Interior Angles Converse
g. Parallel Lines: The lines that $\angle4$ and $\angle21$ are formed on; Converse: Corresponding Angles Converse
h. Parallel Lines: The lines that $\angle8$ and $\angle18$ are formed on; Converse: Same - Side Interior Angles Converse
i. Parallel Lines: The lines that $\angle5$ and $\angle15$ are formed on; Converse: Corresponding Angles Converse