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Grade 7 STEM

Triangle Properties & Pythagoras Lab

Interactive CBSE Class 7 Mathematics laboratory (NCERT Chapter 6). Explore the angle sum property (180°), exterior angle theorem, triangle inequality limits, and experience an interactive visual square-tiling proof of the Pythagoras Theorem.

CBSE Grade 7 NCERT Ch 6 Geometry Studio
Interactive Canvas — Drag vertices A, B, or C ∠A + ∠B + ∠C = 180.0°
Geometry Telemetry & Classification
Classification by Sides
Scalene
Classification by Angles
Acute-angled
Interior Angles:
∠A (Vertex A): 60.0°
∠B (Vertex B): 60.0°
∠C (Vertex C): 60.0°
Total Angle Sum: 180.0°
Side Lengths:
Side a (opposite A / BC): 12.0 cm
Side b (opposite B / AC): 12.0 cm
Side c (opposite C / AB): 12.0 cm
Perimeter (P): 36.0 cm
NCERT Rule: Drag any vertex anywhere on the canvas — the sum of the three interior angles will always remain exactly 180°!
Exterior Angle Theorem Studio — Side BC is extended to D Exterior = Sum of Interior Opposite Angles
Theorem Verification
Exterior Angle Property:
∠ACD = ∠A + ∠B
An exterior angle of a triangle is equal to the sum of its two interior opposite angles.
Interior Opposite ∠A: 50.0°
Interior Opposite ∠B: 70.0°
Sum (∠A + ∠B): 120.0°
Exterior ∠ACD: 120.0°
Proof Derivation:
• ∠A + ∠B + ∠ACB = 180° (Angle Sum)
• ∠ACB + ∠ACD = 180° (Linear Pair on BCD)
• Equating both equations:
∠A + ∠B + ∠ACB = ∠ACB + ∠ACD
⇒ ∠ACD = ∠A + ∠B (Proven!)
Stick Assembly Simulator Triangle Can Be Formed
Stick Length Sliders
NCERT Sum of Any Two Sides > Third Side:
1. a + b > c: 8.0 + 10.0 = 18.0 > 12.0 ✓
2. b + c > a: 10.0 + 12.0 = 22.0 > 8.0 ✓
3. c + a > b: 12.0 + 8.0 = 20.0 > 10.0 ✓
✓ Triangle Possible
All three inequality conditions are satisfied. The two rotating sticks can touch to close the vertex!
h = 5.0
Square Tiling Proof: Area(b) + Area(p) = Area(h) 9 + 16 = 25
Pythagoras Equation Solver
NCERT Step-by-Step Working:
h² = b² + p²
h² = 3² + 4² = 9 + 16 = 25
h = √25 = 5
Calculated Length: h = 5.0 units
CBSE Class 7 Mathematics: Chapter 6 Notes
1. Medians & Altitudes of a Triangle
  • Median: A line segment connecting a vertex of a triangle to the mid-point of the opposite side. A triangle has 3 medians that intersect at a single point called the Centroid (G).
  • Altitude: The perpendicular line segment drawn from a vertex to the opposite side (or line containing the opposite side). The 3 altitudes meet at the Orthocenter (H).
2. Angle Sum & Exterior Angle Properties
• ∠A + ∠B + ∠C = 180°
• Exterior Angle = Sum of two interior opposite angles

These two theorems are fundamental. If you know any two interior angles of a triangle, the third angle is simply 180° minus their sum.

3. Triangle Inequality Property
a + b > c,  b + c > a,  c + a > b

The sum of the lengths of any two sides of a triangle must be strictly greater than the length of the third side. Conversely, the difference between the lengths of any two sides is always smaller than the third side!

4. Pythagoras Property (Right Triangles)
(Hypotenuse)² = (Base)² + (Perpendicular)²
h² = b² + p²

In a right-angled triangle, the side opposite the 90° right angle is the longest side, called the Hypotenuse. This theorem was also documented in ancient Indian geometry in the Baudhayana Sulba Sutras.