Week 11 · Angles and their relations: types, angle pairs, transversal names · 3 lessons
3
Two lines and a transversal: corresponding, alternate and interior angles
Mathematics Prep 1 Term 1, Unit 4, Lessons 1–2
GoalRecognise corresponding, alternate and same-side interior angles in a figure.
New words
transversal · a line that cuts two or more other linescorresponding · angles in the same position at the two crossingsalternate · interior angles on opposite sides of the transversalinterior angles · the four angles between the two lines
Explanation
A transversal is a line that cuts two other lines. It makes eight angles. The four between the two lines are interior and the four outside are exterior. We name the pairs by their position. Corresponding angles are in the same place at the two crossings, such as the upper left at each crossing. Alternate angles are interior angles on opposite sides of the transversal. Interior angles on the same side of the transversal are next to each other on one side. In the figure the two lines are parallel (marked with arrows) and the angles are numbered 1 to 8. Naming the pairs does not need any numbers; the size rules come in the next lesson.
Worked examples
Corresponding angles. In the figure angles 1 and 5 are both the upper left at their crossing, so they are corresponding. So are 2 and 6, 3 and 7, 4 and 8.
Alternate angles. The interior angles are 3, 4, 5 and 6. Angles 4 and 5 are interior and on opposite sides of the transversal, so they are alternate angles. So are 3 and 6.
Same-side interior angles. Angles 3 and 5 are both interior and both on the left of the transversal. So are 4 and 6 on the right. The exterior angles are 1, 2, 7 and 8.
Class activity
Find the pairs. With a grown-up, draw two lines and a transversal on paper and number the eight angles. Colour all the corresponding pairs in one colour each. Then find the alternate pairs and the same-side pairs.
Practice
1
In the figure, what are angles 1 and 5 called?
Corresponding angles.
2
What are angles 4 and 5 called?
Alternate angles (interior, opposite sides).
3
What are angles 3 and 5 called?
Interior angles on the same side of the transversal.
4
Name the four exterior angles.
Angles 1, 2, 7 and 8.
5
Hana says angles 3 and 6 are corresponding. What is wrong?
They are interior angles on opposite sides of the transversal, so they are alternate angles. Corresponding angles are in the same position, like 3 and 7.
