Transversal — Grade 8 Math, what it means and where it is taught
A line that crosses two or more other lines.
Taught in Grade 8 Math.
Where it is taught
What uses it later
This idea is needed for:
- Alternate interior angles — Between the parallels, on opposite sides of the transversal. Equal.
Practise this idea
7 questions in the course bank use Transversal, in Geometric Construction, Angle Relationships, How to Write a Proof.
Problem 1
Two parallel lines are cut by a transversal. One angle is 73°. Find the co-interior angle on the same side.
Worked answer
107
180 - 73 = 107°
Problem 2
Two parallel lines are cut by a transversal. One angle is 64°. Find its corresponding angle.
Worked answer
64
Same position at the other crossing
64°
Problem 3
Two parallel lines are cut by a transversal. One angle is 110°. Find the co-interior angle on the same side.
Worked answer
70
180 - 110 = 70
70°
Problem 4
Two parallel lines are cut by a transversal. Corresponding angles measure (2x + 15)° and (4x - 25)°. Find x.
Worked answer
20
2x + 15 = 4x - 25
40 = 2x
x = 20
Problem 5
Which pair of angles is not necessarily equal when two parallel lines are cut by a transversal?
- Co-interior angles
- Corresponding angles
- Alternate interior angles
- Vertical angles
Worked answer
Co-interior angles
Co-interior angles are supplementary, not equal
They are only equal in the special case of 90° each
Problem 6
Two parallel lines are cut by a transversal. One angle is (5x - 10)° and the co-interior angle is (3x + 6)°. Find both angles.
Worked answer
105 and 75
5x - 10 + 3x + 6 = 180
8x = 184, so x = 23
5(23) - 10 = 105 and 3(23) + 6 = 75
Check: 105 + 75 = 180 ✓
Problem 7
You are given that AB ∥ CD. What angle relationship does a transversal give you?
Worked answer
congruent alternate interior angles
Alternate interior angles are congruent.
Corresponding angles are congruent too.