Class 7 | Ganita Prakash | Chapter 5
📏 Parallel & Intersecting Lines
Angles · Transversals · Parallel Lines
📏 5.1 — Intersecting Lines
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Lines that cross = Intersecting Lines
When two lines cross, they form 4 angles!
When two lines cross, they form 4 angles!
- The point where they meet = Point of Intersection
- Angles across from each other = Vertically Opposite Angles
- Vertically opposite angles are ALWAYS EQUAL! ✅
✂️ Like scissors!
When scissors open, the two blades form intersecting lines!
The angle between them = the angle at which they cut!
When scissors open, the two blades form intersecting lines!
The angle between them = the angle at which they cut!
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⊥ 5.2 — Perpendicular Lines
Perpendicular Lines:
Lines that intersect at exactly 90° (right angle)
Symbol: ⊥ (Line AB ⊥ Line CD)
Examples in real life:
Lines that intersect at exactly 90° (right angle)
Symbol: ⊥ (Line AB ⊥ Line CD)
Examples in real life:
- Walls and floor
- Door frame corners
- Edges of a notebook
- + sign in math!
Right angle = 90° EXACTLY
If two lines make a 90° angle → they are perpendicular
We draw a small □ to show a right angle in diagrams
If two lines make a 90° angle → they are perpendicular
We draw a small □ to show a right angle in diagrams
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↔️ 5.3 — Angles Between Lines
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| Angle Type | Measure | Example |
|---|---|---|
| Acute | 0° to 90° | 45°, 30°, 60° |
| Right | Exactly 90° | Corner of book |
| Obtuse | 90° to 180° | 115°, 135° |
| Straight | Exactly 180° | A straight line |
| Reflex | 180° to 360° | 270°, 300° |
Linear Pair: Two angles on a straight line add up to 180°
If angle 1 = 70°, then angle 2 = 110° (because 70+110=180)
If angle 1 = 70°, then angle 2 = 110° (because 70+110=180)
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↗️ 5.5 — Transversals
What is a Transversal?
A line that cuts across two or more other lines
When a transversal cuts two parallel lines, it creates 8 angles!
A line that cuts across two or more other lines
When a transversal cuts two parallel lines, it creates 8 angles!
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🔷 5.6 — Corresponding Angles
When a transversal cuts PARALLEL lines:
Corresponding angles = same position at each intersection
→ They are EQUAL! ✅
Think of it as: Same angle, just moved up or down the transversal!
Corresponding angles = same position at each intersection
→ They are EQUAL! ✅
Think of it as: Same angle, just moved up or down the transversal!
🏗️ Real Life — Railway tracks!
Railway tracks = parallel lines
A road crossing them = transversal
The angles the road makes with both tracks = corresponding angles (equal!)
Railway tracks = parallel lines
A road crossing them = transversal
The angles the road makes with both tracks = corresponding angles (equal!)
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🔶 5.8 — Alternate Angles
Alternate angles: On opposite sides of the transversal
→ Always EQUAL when lines are parallel ✅
Alternate Interior: Between the parallel lines (Z-shape!)
Alternate Exterior: Outside the parallel lines (Z-shape too!)
→ Always EQUAL when lines are parallel ✅
Alternate Interior: Between the parallel lines (Z-shape!)
Alternate Exterior: Outside the parallel lines (Z-shape too!)
Z-shape trick! 🔤
Draw a Z between two parallel lines — the angles at the corners are alternate angles and they're always equal!
Also called "Z-angles"!
Draw a Z between two parallel lines — the angles at the corners are alternate angles and they're always equal!
Also called "Z-angles"!
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📝 Quick Summary
Intersecting lines
cross at a point
form 4 angles!
cross at a point
form 4 angles!
Perpendicular = 90°
Symbol: ⊥
Right angle!
Symbol: ⊥
Right angle!
Transversal cuts
parallel lines →
8 special angles!
parallel lines →
8 special angles!
Corresponding ✅=
Alternate ✅=
(Parallel lines!)
Alternate ✅=
(Parallel lines!)
| Angle Pair | Relation | Condition |
|---|---|---|
| Vertically Opposite | Equal | Always |
| Linear Pair | Add to 180° | Always |
| Corresponding | Equal | Lines must be parallel |
| Alternate Interior | Equal | Lines must be parallel |
| Co-interior (same side) | Add to 180° | Lines must be parallel |
🌟 Chapter 5 Complete! 🌟
Made with ❤️ by @edugrown
Made with ❤️ by @edugrown