Maharashtra Board Class 9 Maths Part 2 Geometry Chapter 1 Basic Concepts in Geometry Set 1.3 Solutions

Question 1. Write the following statements in 'if-then' form.
(i) The opposite angles of a parallelogram are congruent.
(ii) The diagonals of a rectangle are congruent.
(iii) In an isosceles triangle, the segment joining the vertex and the midpoint of the base is perpendicular to the base.
Answer:
(i) If a quadrilateral is a parallelogram, then its opposite angles are congruent.
(ii) If a quadrilateral is a rectangle, then its diagonals are congruent.
(iii) If a triangle is isosceles triangle, then segment joining the vertex of a triangle and midpoint of the base is perpendicular to the base.
In simple words: This question asks to rewrite given statements in a logical 'if-then' conditional form, identifying the hypothesis and conclusion for each geometric property.

🎯 Exam Tip: Understanding how to convert statements into 'if-then' form is crucial for proving theorems and understanding geometric logic, often carrying marks for correct conditional structure.

Question 2. 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.
Answer:
(i) If the alternate angles made by two lines and their transversal are congruent, then the two lines are parallel.
(ii) If two parallel lines are intersected by a transversal, then the interior angles formed by the transversal are supplementary.
(iii) If the diagonals of a quadrilateral are congruent, then that quadrilateral is a rectangle.
In simple words: This question requires stating the converse of given geometric statements, which involves swapping the hypothesis and conclusion of the original statement.

🎯 Exam Tip: Being able to accurately write converses demonstrates a deeper understanding of geometric properties and their logical inversions, which is a common requirement in proofs and logical reasoning questions.