Write the converse of the given conditional statements:
a. If a pair of the interior angles made by a transversal of two lines are supplementary, then the lines are parallel.

b. If the corresponding angles formed by a transversal of two lines are congruent then the two lines are parallel.

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Solution

a. If two parallel lines are intersected by a transversal, then the interior angles formed by the transversal are supplementary.

b. If two lines are parallel, then the corresponding angles formed by a transversal of two lines are congruent.

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Similar questions

Write converses of the following statements.

(i) The alternate angles formed by two parallel lines and their transversal are congruent.

(ii) If a pair of the interior angles made by a transversal of two lines are supplementary then the lines are parallel.

(iii) The diagonals of a rectangle are congruent.

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.

Q. 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 away that a pair of alternate angles are equal, then the lines are ...
(vi) If a transversal intersects a pair of lines in such away that the sum of interior angles on the same side of transversal is 180°, then the lines are ...

Q. State the following statement is True or False
The corresponding angle converse theorem states that :
If two parallel lines are cut by Transversal then the pair of corresponding angles are congruent

Q. if two lines are intersected by a transversal such that the pair of interior angle on the same side of the transversal are supplementary then prove that the lines are parallel

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Write the converse of the given conditional statements: a. If a pair of the interior angles made by a transversal of two lines are supplementary, then the lines are parallel. b. If the corresponding angles formed by a transversal of two lines are congruent then the two lines are parallel.

a. If two parallel lines are intersected by a transversal, then the interior angles formed by the transversal are supplementary. b. If two lines are parallel, then the corresponding angles formed by a transversal of two lines are congruent.

Write the converse of the given conditional statements:
a. If a pair of the interior angles made by a transversal of two lines are supplementary, then the lines are parallel.

b. If the corresponding angles formed by a transversal of two lines are congruent then the two lines are parallel.

a. If two parallel lines are intersected by a transversal, then the interior angles formed by the transversal are supplementary.

b. If two lines are parallel, then the corresponding angles formed by a transversal of two lines are congruent.