Class 7 | Ganita Prakash | Chapter 7
🔺 A Tale of Three Lines (Triangles)
Types · Altitudes · Construction · Angles
🔺 7.1 — Equilateral Triangles
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@edugrown
Equilateral Triangle:
- All 3 sides are EQUAL
- All 3 angles are EQUAL = 60° each
- 3 × 60° = 180° ✅ (triangle angle sum!)
- It has 3 lines of symmetry
🏕️ A tent is a triangle!
Many tents use equilateral triangle shapes — they're the strongest shape!
Engineers use triangles in bridges and towers for maximum stability! 🏗️
Many tents use equilateral triangle shapes — they're the strongest shape!
Engineers use triangles in bridges and towers for maximum stability! 🏗️
Sum of angles in ANY triangle = 180°
This is one of the most important rules in geometry!
If angle A = 70°, angle B = 60°, then angle C = 180 – 70 – 60 = 50°
This is one of the most important rules in geometry!
If angle A = 70°, angle B = 60°, then angle C = 180 – 70 – 60 = 50°
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📐 7.2 — Types by Sides
| Type | Sides | Angles | Example |
|---|---|---|---|
| Equilateral | All 3 equal | All 60° | △ with side 5cm, 5cm, 5cm |
| Isosceles | 2 sides equal | 2 base angles equal | △ with 5cm, 5cm, 3cm |
| Scalene | All 3 different | All different | △ with 3cm, 4cm, 5cm |
Isosceles Triangle property:
The two angles at the BASE (opposite equal sides) are always equal!
If base angles = 50° each, apex angle = 180 – 50 – 50 = 80°
The two angles at the BASE (opposite equal sides) are always equal!
If base angles = 50° each, apex angle = 180 – 50 – 50 = 80°
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📏 7.3 — Constructing Triangles
You need at least 3 of these 6 elements to construct a unique triangle:
(3 sides + 3 angles, but NOT all 3 angles alone)
(3 sides + 3 angles, but NOT all 3 angles alone)
Draw the base using a ruler
Set compass to length of next side, draw arc from one end
Set compass to 3rd side, draw arc from other end
Where arcs cross = the third vertex!
Triangle Inequality Theorem:
Sum of any 2 sides must be GREATER than 3rd side!
3cm + 4cm > 5cm ✅ (valid triangle)
1cm + 2cm > 5cm? → 3 > 5? ❌ (NOT a valid triangle!)
Sum of any 2 sides must be GREATER than 3rd side!
3cm + 4cm > 5cm ✅ (valid triangle)
1cm + 2cm > 5cm? → 3 > 5? ❌ (NOT a valid triangle!)
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⬇️ 7.4 — Altitudes of Triangles
@edugrown
What is an Altitude?
A perpendicular line from a vertex to the opposite side.
A perpendicular line from a vertex to the opposite side.
- Every triangle has 3 altitudes
- All 3 altitudes meet at a point called Orthocentre
- Altitude ⊥ base (makes 90°)
Where is the Orthocentre? 🎯
Acute triangle: Orthocentre is INSIDE
Right triangle: Orthocentre is at the RIGHT ANGLE vertex
Obtuse triangle: Orthocentre is OUTSIDE the triangle!
Acute triangle: Orthocentre is INSIDE
Right triangle: Orthocentre is at the RIGHT ANGLE vertex
Obtuse triangle: Orthocentre is OUTSIDE the triangle!
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🔷 7.5 — Types by Angles
| Type | Angles | Property |
|---|---|---|
| Acute Triangle | All angles < 90° | All 3 altitudes inside |
| Right Triangle | One angle = 90° | Pythagoras theorem applies! |
| Obtuse Triangle | One angle > 90° | One altitude is outside |
🔑 Pythagoras Theorem (for Right Triangles):
Famous right triangles: 3-4-5, 5-12-13, 8-15-17
a² + b² = c²
where c = hypotenuse (longest side, opposite to 90°)Famous right triangles: 3-4-5, 5-12-13, 8-15-17
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📝 Quick Summary
Sum of angles
= 180° always!
A+B+C=180
= 180° always!
A+B+C=180
Equilateral:
All sides equal
All angles 60°
All sides equal
All angles 60°
Altitude ⊥ base
3 altitudes meet
at Orthocentre!
3 altitudes meet
at Orthocentre!
Right triangle:
a²+b²=c²
Pythagoras!
a²+b²=c²
Pythagoras!
| Triangle Type | Sides | Angles |
|---|---|---|
| Equilateral | All equal | All 60° |
| Isosceles | 2 equal | 2 base angles equal |
| Scalene | All different | All different |
| Right | Any | One = 90°, a²+b²=c² |
| Obtuse | Any | One > 90° |
🌟 Chapter 7 Complete! 🌟
Made with ❤️ by @edugrown
Made with ❤️ by @edugrown