Which of the following statements are true (T) and which are false (F) ? Give reasons.

ii. If two parallel lines are intersected by a transversal, then alternate interior angles are equal.

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Solution

Two parallel lines intersected by a transversal have equal alternate interior angles.
From the figure,
$A B | | C D,$ then
$∠ 3 = ∠ 5 and ∠ 4 = ∠ 6$

Hence, the given statements is true.

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Similar questions

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.

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 ___

Q. Which of the following statements are true (T) and which are false (F) ? Give reasons.

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

Q. Which of the following statements are true (T) and which are false (F) ? Give reasons.

i. If two lines are intersected by a transversal, the corresponding angles are equal.

If two parallel lines are intersected by a transversal, then alternate interior angles are equal.

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Interior Angle Theorem and Its Converse

Standard VIII Mathematics

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Which of the following statements are true (T) and which are false (F) ? Give reasons.​ ii. If two parallel lines are intersected by a transversal, then alternate interior angles are equal.​

Two parallel lines intersected by a transversal have equal alternate interior angles. From the figure, AB||CD, then ∠3=∠5 and ∠4=∠6 Hence, the given statements is true.

Which of the following statements are true (T) and which are false (F) ? Give reasons.

ii. If two parallel lines are intersected by a transversal, then alternate interior angles are equal.

Two parallel lines intersected by a transversal have equal alternate interior angles.
From the figure,
$A B | | C D,$ then
$∠ 3 = ∠ 5 and ∠ 4 = ∠ 6$

Hence, the given statements is true.