Topics
Number Systems
Number Systems
Polynomials
Algebra
Algebraic Expressions
Algebraic Identities
Coordinate Geometry
Linear Equations in Two Variables
Coordinate Geometry
Geometry
Area
Constructions
- Introduction of Constructions
- Geometric Constructions
- Some Constructions of Triangles
Introduction to Euclid’S Geometry
Mensuration
Statistics and Probability
Lines and Angles
- Introduction to Lines and Angles
- Basic Terms and Definitions
- Intersecting Lines and Non-intersecting Lines
- Parallel Lines
- Concept of Pairs of Angles
- Concept of Transversal Lines
- Basic Properties of a Triangle
Probability
Triangles
Quadrilaterals
- Properties of Quadrilateral
- Another Condition for a Quadrilateral to Be a Parallelogram
- Theorem of Midpoints of Two Sides of a Triangle
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram
Circles
Areas - Heron’S Formula
- Area of a Triangle by Heron's Formula
- Application of Heron’s Formula in Finding Areas of Quadrilaterals
- Geometric Interpretation of the Area of a Triangle
Surface Areas and Volumes
Statistics
Estimated time: 14 minutes
- Introduction
- Angles Formed by Two Lines and Their Transversal
- When Two Parallel Lines Are Cut by a Transversal
- Example 1
CISCE: Class 6
Introduction
When a straight line intersects two or more other lines, it forms several angles. This intersecting line is known as a transversal.
Transversals are key to understanding many angle relationships, especially when they cross parallel lines. Recognising the types of angles formed helps in solving geometric problems and proving angle theorems.
CISCE: Class 6
Angles Formed by Two Lines and Their Transversal
| Type of Angle | Angle Pairs | Location |
|---|---|---|
| Exterior Angles | 1, 2, 7, 8 | Outside the two lines |
| Interior Angles | 3, 4, 5, 6 | Between the two lines |
| Exterior Alternate Angles | (1, 7), (2, 8) | Opposite sides of the transversal, outside the lines |
| Interior Alternate Angles | (3, 5), (4, 6) | Opposite sides of the transversal, between the lines |
| Corresponding Angles | (1, 5), (2, 6), (3, 7), (4, 8) | Same relative position at each intersection |
| Co-Interior (Allied) Angles | (3, 6), (4, 5) | Same side of the transversal, inside the lines |
| Exterior Allied Angles | (2, 7), (1, 8) | Same side of the transversal, outside the lines |
CISCE: Class 6
When Two Parallel Lines Are Cut by a Transversal
| Type of Angles | Angle Pairs | Relationship / Property | Explanation |
|---|---|---|---|
| Exterior Alternate Angles | (1, 7) and (2, 8) | ∠1 = ∠7 and ∠2 = ∠8 | Exterior alternate angles are equal. |
| Interior Alternate Angles | (3, 5) and (4, 6) | ∠3 = ∠5 and ∠4 = ∠6 | Interior alternate angles are equal. |
| Corresponding Angles | (1, 5), (2, 6), (3, 7), (4, 8) | ∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, ∠4 = ∠8 | Corresponding angles are equal. |
| Co-Interior (Allied) Angles | (4, 5) and (3, 6) | ∠4 + ∠5 = 180°, ∠3 + ∠6 = 180° | Co-interior (allied) angles are supplementary (sum of angles = 180°). |
| Exterior Allied Angles | (2, 7) and (1, 8) | ∠2 + ∠7 = 180°, ∠1 + ∠8 = 180° | Exterior allied angles are supplementary (sum of angles = 180°). |
CISCE: Class 6
Example 1
In the figure given alongside, two parallel lines are cut by a transversal. Find, giving reasons, the values of the angles x, y and z.
Solution:
∠x = 80° [Vertically opposite angles]
∠y = ∠x = 80° [Alternate angles]
∠x + ∠z = 180° [Co-interior angles are supplementary]
80° + ∠z = 180°
=> ∠z = 180° − 80° = 100°
∴ ∠x = 80°, ∠y = 80° and ∠z = 100°
Test Yourself
Video Tutorials
Shaalaa.com | Parallel lines and Transversal
to track your progress
Series:
0%
Parallel lines and Transversal
00:31:58 undefined
00:31:58 undefined
Theorem : If a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.
00:13:41 undefined
00:13:41 undefined
Theorem : If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel.
00:10:55 undefined
00:10:55 undefined
Theorem : If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary.
00:12:44 undefined
00:12:44 undefined
Theorem : If a transversal intersects two lines such that a pair of interior angles on the same side of the transversal is supplementary, then the two lines are parallel.
00:12:59 undefined
00:12:59 undefined
