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Alternate Angles Test

Consider the ...

Question

Consider the following statements relating to $3$ lines $L_{1}, L_{2}$ and $L_{3}$ in the same plane
$1.$ If $L_{2}$ and $L_{3}$ are both parallel to $L_{1}$ , then they are parallel to each other
$2.$ If $L_{2}$ and $L_{3}$ are both perpendicular to $L_{1}$ , then they are parallel to each other
$3.$ If the acute angle between $L_{1}$ and $L_{2}$ is equal to the acute angle between $L_{1}$ and $L_{3}$ then $L_{2}$ is parallel to $L_{3}$ .
Of these statements which one is correct?

1

and

2

are correct

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1

and

3

are correct

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2

and

3

are correct

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1, 2

and

3

are correct

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Solution

The correct option is D $1, 2$ and $3$ are correct
$l_{1} | | l_{2}$ & $l_{2} | | l_{3} \Rightarrow l_{1} | | l_{2} | | l_{3}$
$1)$ is correct
$l_{1} ⊥ l_{2}, l_{1} ⊥ l_{3} \Rightarrow l_{2} | | l_{3}$
$2)$ is correct
$3)$ is also correct. (corresponding angles)

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The correct option is D 1,2 and 3 are correctl1||l2 & l2||l3⇒l1||l2||l31) is correct l1⊥l2,l1⊥l3⇒l2||l32) is correct 3) is also correct. (corresponding angles)

The correct option is D $1, 2$ and $3$ are correct
$l_{1} | | l_{2}$ & $l_{2} | | l_{3} \Rightarrow l_{1} | | l_{2} | | l_{3}$
$1)$ is correct
$l_{1} ⊥ l_{2}, l_{1} ⊥ l_{3} \Rightarrow l_{2} | | l_{3}$
$2)$ is correct
$3)$ is also correct. (corresponding angles)