Constructions of Triangles — Class 9 Maharashtra SSC Mathematics revision notes
A 4-page visual revision sheet for Constructions of Triangles, 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
Constructions of Triangles in one look
compass and straight edge, four standard cases, and the condition that decides whether a triangle exists
The rules, and what must be shown
- only a compass and an ungraduated straight edge may be used to build the figure
- the ruler may be used to set the compass to a given length, but not to mark a point by measuring along a line
- a protractor is not allowed, so every angle must be built from arcs
- all construction arcs must be left showing, since they are the evidence the figure was constructed rather than drawn
- label each point as it is created, and write the steps beside the figure
- a rough sketch of the finished triangle drawn first tells you what you are aiming at and costs almost nothing
The four standard cases
- SSS: three sides given. Draw the longest as the base, then swing an arc of each remaining length from an end. Where the arcs cross is the third vertex
- SAS: two sides and the included angle. Draw one side, construct the angle at one end, cut off the second side along that arm, then join
- ASA: two angles and the included side. Draw the side, construct one angle at each end, and the two arms meet at the third vertex
- RHS: a right angle, the hypotenuse and one side. Draw the known side, erect the perpendicular at one end, then cut the hypotenuse off with an arc from the far end
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Constructions of Triangles sheet covers
- Construction
- Compass and straight edge
- The rules, and what must be shown
- SSS construction
- SAS construction
- ASA construction
- RHS construction
- The four standard cases
- SSS
- SAS
- ASA
- RHS
- When a triangle cannot be built
- Constructing a triangle from three sides
- Building the angles you need
- Perimeter and base angles
- Base, angle and difference of sides
- The harder cases the chapter adds
- What the given data lets you build
- The basic constructions everything uses
- 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 Constructions of Triangles 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.