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Sss Construction
SSS means three given sides and no given angle. You draw one side as a base, then from each endpoint you open a compass to the remaining two lengths and draw arcs. The third vertex is where the arcs meet. The triangle is unique if the three lengths can form a triangle at all. That check is the triangle inequality: each pair of sides must sum to more than the third side.
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Sss Construction
What is it?
SSS means three given sides and no given angle. You draw one side as a base, then from each endpoint you open a compass to the remaining two lengths and draw arcs. The third vertex is where the arcs meet. The triangle is unique if the three lengths can form a triangle at all. That check is the triangle inequality: each pair of sides must sum to more than the third side.
In simple words
- SSS means three given sides and no given angle.
- For sides a, b, c you need a + b > c, b + c > a, and c + a > b: each pair sum > third.
- Draw the longest side as the base so the third vertex sits clearly above it.
- SSS uniqueness is the reason you can copy a triangle with a compass and straightedge when only sides are known.
Important terms
three given sides: SSS means three given sides and no given angle.
arcs: You draw one side as a base, then from each endpoint you open a compass to the remaining two lengths and draw arcs.
unique: The triangle is unique if the three lengths can form a triangle at all.
triangle inequality: That check is the triangle inequality: each pair of sides must sum to more than the third side.
What you should learn
- Explain sss construction in clear mathematical language.
- Use the main rule, formula, test, or construction correctly.
- Work through a simple example and show each important step.
- Identify common mistakes and write an exam-ready conclusion.
Examples
- 3, 4, 5 works (3+4>5, 3+5>4, 4+5>3)
- 3, 4, 8 fails because 3+4 is not greater than 8
- 5, 5, 10 fails: 5+5 = 10, a flat line, not a triangle
TRIANGLE INEQUALITY
For sides a, b, c you need a + b > c, b + c > a, and c + a > b: each pair sum > third. If any pair sums to less than or equal to the third, the arcs never meet in a proper triangle (they miss, or they just kiss on the base). The standard fail example is 3, 4, 8: 3 + 4 = 7, which is less than 8, so no triangle.
HOW TO DRAW SSS
Draw the longest side as the base so the third vertex sits clearly above it. Swing arcs from both ends: from one end, arc of radius equal to the second side; from the other end, arc of radius equal to the third side. Their intersection is the third vertex. Join it to both ends. If the lengths are valid, the two arcs meet at exactly one useful point above the base (and a mirror point below, which is the same triangle flipped).
Recommended for Class 9
Full school-level explanation
SSS means three given sides and no given angle. You draw one side as a base, then from each endpoint you open a compass to the remaining two lengths and draw arcs. The third vertex is where the arcs meet. The triangle is unique if the three lengths can form a triangle at all. That check is the triangle inequality: each pair of sides must sum to more than the third side.
First test the lengths, then swing the arcs:
WHAT — Core idea
SSS means three given sides and no given angle. You draw one side as a base, then from each endpoint you open a compass to the remaining two lengths and draw arcs. The third vertex is where the arcs meet. The triangle is unique if the three lengths can form a triangle at all. That check is the triangle inequality: each pair of sides must sum to more than the third side.
HOW — Rules, method, and examples
1. TRIANGLE INEQUALITY: For sides a, b, c you need a + b > c, b + c > a, and c + a > b: each pair sum > third. If any pair sums to less than or equal to the third, the arcs never meet in a proper triangle (they miss, or they just kiss on the base). The standard fail example is 3, 4, 8: 3 + 4 = 7, which is less than 8, so no triangle. 2. HOW TO DRAW SSS: Draw the longest side as the base so the third vertex sits clearly above it. Swing arcs from both ends: from one end, arc of radius equal to the second side; from the other end, arc of radius equal to the third side. Their intersection is the third vertex. Join it to both ends. If the lengths are valid, the two arcs meet at exactly one useful point above the base (and a mirror point below, which is the same triangle flipped).
WHY — Meaning and connections
SSS uniqueness is the reason you can copy a triangle with a compass and straightedge when only sides are known. Do not invent an angle. If the question gives 3, 4, 8, write 'does not satisfy the triangle inequality' instead of forcing a sketch.
HOW — Answer in an exam
SSS: arcs from both ends of the base. Unique when each pair of sides sums to more than the third. 3, 4, 8 fail. Equal sum (5, 5, 10) is also not a triangle. Check inequality before drawing.
TRIANGLE INEQUALITY
For sides a, b, c you need a + b > c, b + c > a, and c + a > b: each pair sum > third. If any pair sums to less than or equal to the third, the arcs never meet in a proper triangle (they miss, or they just kiss on the base). The standard fail example is 3, 4, 8: 3 + 4 = 7, which is less than 8, so no triangle.
Remember
- each pair sum > third
- 3, 4, 8
Examples
- 3, 4, 5 works (3+4>5, 3+5>4, 4+5>3)
- 3, 4, 8 fails because 3+4 is not greater than 8
- 5, 5, 10 fails: 5+5 = 10, a flat line, not a triangle
HOW TO DRAW SSS
Draw the longest side as the base so the third vertex sits clearly above it. Swing arcs from both ends: from one end, arc of radius equal to the second side; from the other end, arc of radius equal to the third side. Their intersection is the third vertex. Join it to both ends. If the lengths are valid, the two arcs meet at exactly one useful point above the base (and a mirror point below, which is the same triangle flipped).
Remember
- base
- arcs from
- intersection
Examples
- Base 8 cm, then arcs 5 cm and 7 cm from the ends
- Use the same compass opening as the written length, not a guess
- If the arcs miss, go back and check the inequality
Remember
- three given sides
- arcs
- unique
- triangle inequality
- copy a triangle
- does not satisfy
- arcs from both ends
- 3, 4, 8
How the ideas connect
SSS uniqueness is the reason you can copy a triangle with a compass and straightedge when only sides are known. Do not invent an angle. If the question gives 3, 4, 8, write 'does not satisfy the triangle inequality' instead of forcing a sketch.
Deeper understanding
Go beyond memorising Sss Construction. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
SSS uniqueness is the reason you can copy a triangle with a compass and straightedge when only sides are known. Do not invent an angle. If the question gives 3, 4, 8, write 'does not satisfy the triangle inequality' instead of forcing a sketch.
Common mistakes
Exam focus
WHAT
Key Points
HOW
Examples
Exam focus
Quick revision
- three given sides
- arcs
- unique
- triangle inequality
- three given sides: SSS means three given sides and no given angle.
- arcs: You draw one side as a base, then from each endpoint you open a compass to the remaining two lengths
SSS: arcs from both ends of the base. Unique when each pair of sides sums to more than the third. 3, 4, 8 fail. Equal sum (5, 5, 10) is also not a triangle. Check inequality before drawing.
For long answers on Sss Construction: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- three given sides
- arcs
- unique
- triangle inequality
Important formulas
- three given sides
- arcs
- unique
Common exam traps
- Correction: SSS: arcs from both ends of the base.
- Correction: Unique when each pair of sides sums to more than the third.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Correction: SSS: arcs from both ends of the base.
- Mistake
Correction: Unique when each pair of sides sums to more than the third.
- Mistake
Correction: 3, 4, 8 fail.
- Mistake
Correction: Equal sum (5, 5, 10) is also not a triangle.
- Mistake
SSS: arcs from both ends of the base. Unique when each pair of sides sums to more than the third. 3, 4, 8 fail. Equal sum (5, 5, 10) is also not a triangle. Che
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
three given sides
arcs
unique
triangle inequality
SSS means three given sides and no given angle. You draw one side as a base, then from each endpoint you open a compass to the remaining two lengths and draw ar
- Definition
- SSS means three given sides and no given angle. You draw one side as a base, then from each endpoint you open a compass to the remaining two lengths and draw ar
- Example
- 3, 4, 5 works (3+4>5, 3+5>4, 4+5>3)
- Critical warning
- Correction: SSS: arcs from both ends of the base.
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Exam Practice
Define
Q1. Define Sss Construction.
Explain
Q2. Explain: TRIANGLE INEQUALITY.
Example
Q3. Give one clear example of Sss Construction and say why it fits.
Mistake
Q4. State one common mistake students make about Sss Construction.
Exam note
Q5. Write a short exam note on Sss Construction: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.