Basic Concepts in Geometry — Class 9 Maharashtra SSC Mathematics revision notes
A 4-page visual revision sheet for Basic Concepts in Geometry, 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
Basic Concepts in Geometry in one look
points on a line measured by numbers, betweenness, and the axioms everything later rests on
The undefined terms, and why they stay undefined
- point, line and plane are taken as undefined. Every definition must rest on something, and these are where the resting stops
- an axiom is a statement accepted without proof, and a theorem is one proved from the axioms
- a line has no endpoints and extends for ever in both directions
- a ray has one endpoint and goes on for ever the other way, and a segment has two endpoints and a definite length
- so only a segment has a length, which is why questions measure segments and never lines
- collinear points all lie on one line, and points that do not are non collinear
Co-ordinates on a line, and distance
- each point of a line can be matched with exactly one real number, called its co-ordinate
- the distance between two points is the positive difference of their co-ordinates, written d(A,B) = |x - y|
- the modulus bars matter: distance is never negative, so the smaller co-ordinate is subtracted from the larger
- so d(A,B) and d(B,A) are the same number, unlike a difference which changes sign
- if A has co-ordinate -3 and B has 5, then d(A,B) = |-3 - 5| = 8
- two segments are congruent when their lengths are equal, written with the ≅ symbol
Betweenness, stated exactly
- point B lies between A and C when all three are collinear and d(A,B) + d(B,C) = d(A,C)
- both conditions are needed: three points can satisfy the distance sum only if they are on one line, and collinearity alone does not fix the order
- this is written A - B - C, and it is the test a question actually wants when it asks whether a point lies between two others
- the midpoint of a segment is the point of it that is equidistant from both ends
- every segment has exactly one midpoint, and its co-ordinate is the average of the two end co-ordinates
- if the sum of the two smaller distances exceeds the largest, the three points form a triangle instead
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Basic Concepts in Geometry sheet covers
- Point line plane
- Undefined terms
- Axiom
- The undefined terms, and why they stay undefined
- Co-ordinate of a point
- Distance between two points
- Co-ordinates on a line, and distance
- Betweenness
- Midpoint
- Betweenness, stated exactly
- Testing betweenness
- Types of angles
- Complementary and supplementary
- Angles, and how they are grouped
- Conditional statement
- Converse
- Conditional statements and their converses
- The words used for the parts of a figure
- The axioms this chapter states
- Symbols 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 Basic Concepts in Geometry 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.