Quadrilaterals — Class 9 Maharashtra SSC Mathematics revision notes
A 4-page visual revision sheet for Quadrilaterals, written for Class 9 Maharashtra SSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Quadrilaterals in one look
four sides, the family tree they form, and the tests that name a shape from its properties
The starting facts
- a quadrilateral is a closed figure with four sides, four vertices and four angles
- its four interior angles add to 360°
- the reason is simple: one diagonal cuts it into two triangles, and each triangle contributes 180°
- opposite sides are the pairs with no vertex in common, and adjacent sides share one
- the two diagonals join opposite vertices, and much of the chapter is about how they behave
- the sum of the exterior angles, one at each vertex, is 360° as it is for any polygon
The parallelogram, and what follows from it
- a parallelogram is a quadrilateral whose opposite sides are parallel, and that one condition forces all the rest
- opposite sides are equal in length
- opposite angles are equal
- consecutive angles are supplementary, adding to 180°, since they are co-interior between the parallel sides
- the diagonals bisect each other, though they are not equal in general
- each diagonal splits it into two congruent triangles, which is how most of these properties are proved
Tests for a parallelogram
- any one of the following is enough to prove a quadrilateral is a parallelogram
- both pairs of opposite sides parallel, which is the definition itself
- both pairs of opposite sides equal
- both pairs of opposite angles equal
- the diagonals bisect each other
- one pair of opposite sides both equal and parallel, which is the most useful test of all and the one most often overlooked
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Quadrilaterals sheet covers
- Quadrilateral
- Angle sum of a quadrilateral
- The starting facts
- Parallelogram
- Properties of a parallelogram
- The parallelogram, and what follows from it
- Tests for a parallelogram
- Rectangle, rhombus and square
- Rectangle
- Rhombus
- What the diagonals do in each shape
- Trapezium
- Kite
- Midpoint theorem
- Trapezium and kite
- Naming a shape from its diagonals
- The family, from general to special
- Terms in this chapter
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Quadrilaterals the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.