NCERT Solutions Class 9 Maths Chapter 12 — Quadrilaterals#

Chapter 12 (Ganita Manjari Part II) defines a quadrilateral precisely, proves the tests for a parallelogram (the converses of its properties), and uses parallelograms to prove the Midpoint Theorem, its converse, the Centroid Theorem and Varignon’s theorem. It ends by showing that the plane can be tiled with copies of any quadrilateral.

Exercises#

• Exercise Set 12.1 — Adjacent and opposite sides and angles, internal angles, convex and non-convex quadrilaterals (5 questions)
• Exercise Set 12.2 — Rectangles, rhombuses and squares; converses of their properties (4 questions)
• Exercise Set 12.3 — Midpoint Theorem, midpoints in quadrilaterals, the Varignon parallelogram (5 questions)
• Exercise Set 12.4 — Tiling the plane (2 questions)
• End-of-Chapter Exercises — Tiling with triangles, folding, trapezia, trisection, polygon diagonals and angle sums, converses of the Midpoint Theorem (24 questions)

What you will learn#

• What counts as a quadrilateral: convex, non-convex and self-intersecting shapes.
• Tests for parallelograms and properties of rectangles, rhombuses and squares.
• The Midpoint Theorem and its converse, and the Varignon parallelogram.
• Tiling the plane with triangles and quadrilaterals.

Key formulas and results#

• The angles of a quadrilateral add up to 360°.
• Midpoint Theorem: the segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long.
• Joining the midpoints of the sides of any quadrilateral gives a parallelogram (Varignon’s theorem).

Read and revise#

• NCERT Class 9 Maths Chapter 12 (PDF) — the Ganita Manjari Part II chapter itself.
• All Class 9 Maths chapters from Ganita Manjari Part I and Part II.

Frequently asked questions#