Question

problem 3 determining whether lines are parallel
the fence gate at the right is made up of pieces of wood arranged in various directions. suppose ∠1≅∠2. are lines r and s parallel? explain.
yes, .∠1 and ∠2 are angles. if two lines and a transversal form , then the lines are
got it? 3. in problem 3, what is another way to explain why r || s? justify your answer.
problem 4 using algebra
algebra what is the value of x for which a || b?
the two angles are . by the of the , if the angles are
got it? 4. what is the value of w for which c || d?

Explanation:

Problem 3

Step1: Identify angle - type

$\angle1$ and $\angle2$ are corresponding angles. If two lines and a transversal form congruent corresponding angles, then the lines are parallel. Since $\angle1\cong\angle2$, lines $r$ and $s$ are parallel.

Step2: Another way for Problem 3

We can check alternate - interior angles. If we can show that a pair of alternate - interior angles formed by lines $r$, $s$ and a transversal are congruent, then $r\parallel s$.

Problem 4

Step1: Identify angle - type

The two angles are corresponding angles. By the corresponding angles postulate, if two parallel lines are cut by a transversal, corresponding angles are congruent. So, if $a\parallel b$, then $2x + 9=111$.

Step2: Solve for $x$

Subtract 9 from both sides of the equation $2x+9 = 111$:
$2x=111 - 9$
$2x=102$
Divide both sides by 2:
$x = 51$

Problem 4 (Got It?)

Step1: Identify angle - type

The two angles are corresponding angles. By the corresponding angles postulate, if $c\parallel d$, then $3w-2 = 55$.

Step2: Solve for $w$

Add 2 to both sides of the equation $3w - 2=55$:
$3w=55 + 2$
$3w=57$
Divide both sides by 3:
$w = 19$

Answer:

For Problem 3: Lines $r$ and $s$ are parallel because $\angle1$ and $\angle2$ are corresponding angles and $\angle1\cong\angle2$. Another way is to check alternate - interior angles.
For Problem 4: $x = 51$
For Problem 4 (Got It?): $w = 19$