A transversal intersects two given lines in such a way that the interior angles on the same side of the transversal are equal. Is it always true that the given lines are parallel? If not, state the condition(s) under which the two lines will be parallel.

True

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False

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Solution

The correct option is A True
From the figure
$x + 1 = 180^{\circ} y + 2 = 180^{\circ}$
Adding above equations
$x + y + 1 + 2 = 360^{\circ}$
given $x + y = 1 + 2$
$x + y + x + y = 360^{\circ} 2 (x + y) = 360^{\circ} x + y = 180^{\circ}$
Angles made on same side of transversal is supplementary . So the lines are parallel
So the statement is true

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Similar questions

Fill in the blanks in each of the following to make the statement true:
(i) If two parallel lines are intersected by a transversal then each pair of corresponding angles are ___
(ii) If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are ___
(iii) Two lines perpendicular to the same line are ___ to each other.
(iv) Two lines parallel to the same line are to ___ each other.

(v) If a transversal intersects a pair of lines in such a way that a pair of alternate angles are equal, then the lines are ___
(vi) If a transversal intersects a pair of lines in such a way that the sum of interior angles on the same side of transversal is $180^{0}$ , then the lines are ___

Which of the following statements are true (I) and which are false (F)? Give reasons.
(i) If two lines are intersected by a transversal, then corresponding angles are equal.
(ii) If two parallel lines are intersected by a transversal, then alternate interior angles are equal.
(iii) Two lines perpendicular to the same line are perpendicular to each other.
(iv) Two lines parallel to the same line are parallel to each other.
(v) If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.

If a transversal intersects a pair of lines in such a way that the sum of interior angles on the same side of transversal is 180 $^{\circ}$ , then the lines are__.

Q. If a transversal intersects two lines such that a pair of alternate interior angles is equal , then the two lines are parallel.

Q. State true or false:

If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are supplementary

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A transversal intersects two given lines in such a way that the interior angles on the same side of the transversal are equal. Is it always true that the given lines are parallel? If not, state the condition(s) under which the two lines will be parallel.

The correct option is A TrueFrom the figurex+1=180∘y+2=180∘Adding above equationsx+y+1+2=360∘given x+y=1+2x+y+x+y=360∘2(x+y)=360∘x+y=180∘Angles made on same side of transversal is supplementary . So the lines are parallelSo the statement is true