Class 7 | Ganita Prakash | Chapter 5
๐ Parallel & Intersecting Lines
Angles ยท Transversals ยท Parallel Lines
๐ 5.1 โ 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! โ
โ๏ธ 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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โฅ 5.2 โ Perpendicular Lines
Perpendicular Lines:
Lines that intersect at exactly 90ยฐ (right angle)
Symbol: โฅ (Line AB โฅ Line CD)
Examples in real life:
Lines that intersect at exactly 90ยฐ (right angle)
Symbol: โฅ (Line AB โฅ Line CD)
Examples in real life:
- Walls and floor
- Door frame corners
- Edges of a notebook
- + sign in math!
Right angle = 90ยฐ EXACTLY
If two lines make a 90ยฐ angle โ they are perpendicular
We draw a small โก to show a right angle in diagrams
If two lines make a 90ยฐ angle โ they are perpendicular
We draw a small โก to show a right angle in diagrams
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โ๏ธ 5.3 โ Angles Between Lines
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| Angle Type | Measure | Example |
|---|---|---|
| Acute | 0ยฐ to 90ยฐ | 45ยฐ, 30ยฐ, 60ยฐ |
| Right | Exactly 90ยฐ | Corner of book |
| Obtuse | 90ยฐ to 180ยฐ | 115ยฐ, 135ยฐ |
| Straight | Exactly 180ยฐ | A straight line |
| Reflex | 180ยฐ to 360ยฐ | 270ยฐ, 300ยฐ |
Linear Pair: Two angles on a straight line add up to 180ยฐ
If angle 1 = 70ยฐ, then angle 2 = 110ยฐ (because 70+110=180)
If angle 1 = 70ยฐ, then angle 2 = 110ยฐ (because 70+110=180)
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โ๏ธ 5.5 โ 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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๐ท 5.6 โ Corresponding Angles
When a transversal cuts PARALLEL lines:
Corresponding angles = same position at each intersection
โ They are EQUAL! โ
Think of it as: Same angle, just moved up or down the transversal!
Corresponding angles = same position at each intersection
โ They are EQUAL! โ
Think of it as: Same angle, just moved up or down the transversal!
๐๏ธ Real Life โ 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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๐ถ 5.8 โ Alternate Angles
Alternate angles: On opposite sides of the transversal
โ Always EQUAL when lines are parallel โ
Alternate Interior: Between the parallel lines (Z-shape!)
Alternate Exterior: Outside the parallel lines (Z-shape too!)
โ Always EQUAL when lines are parallel โ
Alternate Interior: Between the parallel lines (Z-shape!)
Alternate Exterior: Outside the parallel lines (Z-shape too!)
Z-shape trick! ๐ค
Draw a Z between two parallel lines โ the angles at the corners are alternate angles and they're always equal!
Also called "Z-angles"!
Draw a Z between two parallel lines โ the angles at the corners are alternate angles and they're always equal!
Also called "Z-angles"!
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๐ Quick Summary
Intersecting lines
cross at a point
form 4 angles!
cross at a point
form 4 angles!
Perpendicular = 90ยฐ
Symbol: โฅ
Right angle!
Symbol: โฅ
Right angle!
Transversal cuts
parallel lines โ
8 special angles!
parallel lines โ
8 special angles!
Corresponding โ
=
Alternate โ =
(Parallel lines!)
Alternate โ =
(Parallel lines!)
| Angle Pair | Relation | Condition |
|---|---|---|
| Vertically Opposite | Equal | Always |
| Linear Pair | Add to 180ยฐ | Always |
| Corresponding | Equal | Lines must be parallel |
| Alternate Interior | Equal | Lines must be parallel |
| Co-interior (same side) | Add to 180ยฐ | Lines must be parallel |
๐ Chapter 5 Complete! ๐
Made with โค๏ธ by @edugrown
Made with โค๏ธ by @edugrown