F.1 Transversals: name angle pairs

Transversals: name angle pairs

Transversals: Name Angle Pairs by Delta publications

key notes :

🔹 Transversal

A transversal is a line that intersects two or more lines at distinct points.

Example: If line l and line m are cut by a line t, then t is the transversal.

🔹 Angle Pairs Formed by a Transversal

When a transversal cuts two lines, 8 angles are formed. These angles can be grouped into special pairs:

1. Corresponding Angles

Definition: Angles that are on the same side of the transversal and in the same relative position at each intersection.
Example: ∠1 and ∠5, ∠2 and ∠6.
Property: If lines are parallel, corresponding angles are equal.

2. Alternate Interior Angles

Definition: Angles that lie inside the two lines but on opposite sides of the transversal.
Example: ∠3 and ∠6, ∠4 and ∠5.
Property: If lines are parallel, alternate interior angles are equal.

3. Alternate Exterior Angles

Definition: Angles that lie outside the two lines but on opposite sides of the transversal.
Example: ∠1 and ∠8, ∠2 and ∠7.
Property: If lines are parallel, alternate exterior angles are equal.

4. Consecutive Interior Angles (Co-interior / Same-side Interior Angles)

Definition: Angles that lie inside the two lines and are on the same side of the transversal.
Example: ∠3 and ∠5, ∠4 and ∠6.
Property: If lines are parallel, consecutive interior angles are supplementary (sum = 180°).

5. Vertically Opposite Angles

Definition: When two lines intersect, the angles opposite each other are called vertically opposite angles.
Example: ∠1 and ∠3, ∠2 and ∠4.
Property: Vertically opposite angles are always equal (no need for parallel lines).

🔹 Summary of Angle Pair Properties

Angle Pair	Position	Condition	Relationship
Corresponding	Same side, same position	Parallel lines	Equal
Alternate Interior	Inside, opposite sides	Parallel lines	Equal
Alternate Exterior	Outside, opposite sides	Parallel lines	Equal
Consecutive Interior	Inside, same side	Parallel lines	Supplementary (sum = 180°)
Vertically Opposite	Opposite angles at intersection	Always true	Equal

🔹 Diagram (for teaching aid)

You can draw two parallel lines (l, m) cut by a transversal (t) and label angles 1–8. Then use it to show angle pairs.

✅ Key Points for Students:

Learn the names and positions of angle pairs.
Remember that special angle relationships hold true only when the lines are parallel (except vertically opposite angles).
Practice identifying angle pairs in given figures.

Two angles are vertical angles if they are formed by intersecting lines and are not adjacent.

∠AEB and ∠DEC are vertical angles.

A transversal is a line that intersects two other lines.

Two angles formed by a transversal crossing two lines are corresponding angles if they are in matching corners.

∠YXU and ∠VUS are corresponding angles. They are in matching corners.

Two angles are adjacent angles if they have the same vertex and a common side, but no common interior points.

∠ADB and ∠BDC are adjacent angles.

Two angles are supplementary angles if their measures add up to 180°.

∠ABD and ∠DBC are supplementary angles.

A transversal is a line that intersects two other lines.

Two angles formed by a transversal crossing two lines are alternate interior angles if they are between the two lines and are on opposite sides of the transversal, but are not adjacent.

∠KJG and ∠FGJ are alternate interior angles.

A transversal is a line that intersects two other lines.

Two angles formed by a transversal crossing two lines are alternate exterior angles if they are between the two lines and are on opposite sides of the transversal, but are not adjacent.