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.

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Solution

(i) If the alternate angles made by the transversal with the two lines are congruent, then the lines are parallel.

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

(iii) If the diagonals of a quadrilateral are congruent, then that quadrilateral is a rectangle.

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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.

Q. The alternate interior angles are congruent when the transversal intersects two parallel lines.

If two parallel lines are intersected by a transversal then, pair of alternate interior angles are:

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. Read the following statements which are taken as axioms :
(i) If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.
(ii) If a transversal intersect two parallel lines, then alternate interior angles are equal.
Is this system of axioms consistent?

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