Chapter 8 · Class IX Mathematics · NCERT Exercises

Quadrilaterals — Exercises

Parallelogram Properties & Mid-Point Theorem — Both Exercises Solved

📂 2 Exercises 📝 19 Questions 🎓 Moderate-High

▶ Start Exercises 📖 Revise Notes

Exercise Index

①

Exercise 8.1

Properties of parallelogram; opposite sides & angles equal; diagonals bisect each other; converse theorems

12 Q Moderate

②

Exercise 8.2

Mid-Point Theorem; line through midpoints of two sides is parallel to third side and half its length

7 Q Hard

2 exercise files · 19 total questions

Chapter at a Glance

CBSE BoardsNTSEOlympiad

10 Concepts

7 Formulas

Moderate-High Difficulty

10–12% Weightage

Before You Begin

Prerequisites

✓Triangle congruence (Chapter 7)
✓Properties of parallel lines
✓Basic quadrilateral types

Have Ready

🔧Compass and ruler
🔧Parallelogram properties reference card

Exercise Topic Map

Exercise 8.1 Apply: opp sides equal; opp angles equal; diagonals bisect each other; and their converses to identify or prove parallelograms

Exercise 8.2 Mid-Point: if M,N are midpoints of AB,AC then MN∥BC and MN=½BC; converse: line from midpoint parallel to one side bisects the third

Key Formulae — Recall Before Solving

\(ABCD \text{ is }\| \text{gram} \iff AB\|CD,\; AB=CD \quad \text{(opp sides equal \& parallel)}\)

\(\text{Diagonals of parallelogram bisect each other (and converse)}\)

\(\text{Mid-Point Theorem: } MN \parallel BC \text{ and } MN = \tfrac{1}{2}BC\)

\(\text{Angle sum of quadrilateral} = 360°\)

NCERT Solving Method

Step 1 — Parallelogram proofs: use one of four conditions to prove — (i) both pairs of opp sides equal, (ii) both pairs parallel, (iii) diagonals bisect each other, (iv) one pair of sides both equal and parallel. Step 2 — Always draw and label the diagonal(s); most proofs split the quadrilateral into triangles. Step 3 — Mid-Point Theorem: draw the figure with midpoints; extend MN to meet the parallel; form congruent triangles. Step 4 — Angle sum: if three angles are known, fourth = 360° − sum of three. Step 5 — Rectangle/Rhombus/Square: these are special parallelograms; additional properties apply (diagonals equal for rectangle; diagonals perpendicular for rhombus).