1. Basic Concepts in Geometry

1. Write the following statements in ‘if-then’ form:

(i) The opposite angles of a parallelogram are congruent.

Solution:

If a quadrilateral is a parallelogram, then its opposite angles are congruent.

(ii) The diagonals of a rectangle are congruent.

Solution:

If a quadrilateral is a rectangle, then its diagonals are congruent.

(iii) In an isosceles triangle, the segment joining the vertex and the midpoint of the base, is perpendicular to the base.

Solution:

If a triangle is an isosceles triangle, then the segment joining the vertex and the midpoint of the base is perpendicular to the base.

2. Write the converse of the following statements:

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

Converse:

If the alternate angles formed by two lines and their transversal are congruent, then the lines are parallel.

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

Converse:

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

(iii) The diagonals of a rectangle are congruent.

Converse:

If the diagonals of a quadrilateral are congruent, then the quadrilateral is a rectangle.

Lesson 1 : Main Page

Standard 9 : Main Page

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13 April 2026 at 14:43