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L-11, Ch-8th,

📘 Class 9 Maths Chapter 8 – Quadrilaterals | Full Chapter Summary In this chapter, "Quadrilaterals", we study different types of quadrilaterals, their properties, and important theorems related to their sides, angles, and diagonals. This chapter helps build a strong base for higher geometry topics like parallelograms, cyclic quadrilaterals, and proofs in Class 10 and beyond. 🔹 1. Basic Definitions Quadrilateral → A polygon with 4 sides, 4 vertices, 4 angles. Diagonal → A line segment joining any two non-adjacent vertices of a quadrilateral. Angle Sum Property → The sum of the four interior angles of a quadrilateral is always 360°. 🔹 2. Types of Quadrilaterals Parallelogram → Opposite sides are parallel and equal. Rectangle → Parallelogram with all angles = 90°. Square → Rectangle with all sides equal. Rhombus → Parallelogram with all sides equal. Trapezium → Exactly one pair of opposite sides parallel. Kite → Two pairs of adjacent sides equal. 🔹 3. Properties of a Parallelogram Opposite sides are equal and parallel. Opposite angles are equal. Diagonals bisect each other. Each diagonal divides the parallelogram into two congruent triangles. 🔹 4. Theorems on Parallelograms Theorem 8.1: Diagonals of a parallelogram bisect each other. Theorem 8.2: In a parallelogram, opposite sides are equal. Theorem 8.3: In a parallelogram, opposite angles are equal. Theorem 8.4: A diagonal of a parallelogram divides it into two congruent triangles. Theorem 8.5: If in a quadrilateral, diagonals bisect each other, then it is a parallelogram. 🔹 5. Conditions for a Quadrilateral to be a Parallelogram A quadrilateral is a parallelogram if: Both pairs of opposite sides are equal, OR Both pairs of opposite angles are equal, OR One pair of opposite sides is equal and parallel, OR Diagonals bisect each other. 🔹 6. Mid-Point Theorem The line joining the mid-points of two sides of a triangle is: Parallel to the third side, and Equal to half of the third side. 🎯 Key Learning Outcomes Understanding types of quadrilaterals and their properties. Proving important theorems about sides, angles, and diagonals. Using conditions to verify if a quadrilateral is a parallelogram. Applying Mid-point theorem in problems and proofs. Building a strong foundation for coordinate geometry and cyclic quadrilaterals in higher classes. 📥 Like, Share & Subscribe for more NCERT Class 9 Maths summaries, solved examples, and problem-solving guides! 📌  #Class9Maths #Quadrilaterals #NCERTMaths #CBSEClass9 #ParallelogramTheorems #NCERTSolutions #CBSE2025 #MathsWithSahil #MathsChapter8 #MathsRevision #GeometryClass9 #MidPointTheorem #LearnMaths #MathsTricks #CBSEBoard2025 #MathsForBeginners #SchoolMaths #BoardExamPreparation #Class9FullChapter #MotionMaths #MathsConcepts #NCERTGeometry #StudyWithMe #EduYouTube