GCSE · Maths · AQA · Spec 8300 · Foundation
Alternate and corresponding angles on parallel lines
Cut across two parallel lines with one straight line, and the top crossing makes exactly the same angles as the bottom one. Measure one angle and you know several more.
Angles on parallel lines
Alternate angles
AB ∥ CD, so ∠BPQ = ∠CQP in every position
AB and CD are parallel. The line PQ that crosses them is called a transversal. Drag P along AB or Q along CD to tilt and slide it, and keep an eye on the two readouts.
Now change the lines
Corresponding angles
∠BPQ = ∠DQF only while QD is parallel to AB
This time the transversal EF stays put and so does AB. Drag D up or down to turn the lower line QD about Q. The faint line shows where QD is parallel to AB. Watch ∠BPQ and ∠DQF as QD leaves the faint line, and again as you bring it back.
Name the pair
Alternate, corresponding or neither?
AB and CD are parallel, with A and C on the left. The transversal EF crosses AB at P and CD at Q, with E above AB and F below CD. Pick a pair, then choose its name.
Still to sort
Alternate (0)
Both angles are between the parallel lines, on opposite sides of the transversal.
Where the line is: Both angles must be between the lines. If either one is outside them, the pair cannot be alternate.
Corresponding (0)
The same position at each crossing, such as above the line and right of the transversal both times.
Where the line is: Same side of the transversal AND same side of its own line. Opposite sides of the transversal is never corresponding.
Neither (0)
In neither position. Neither name fits, so the equal-angle facts in this lesson say nothing about this pair.
Where the line is: Alternate and corresponding pairs always take one angle from each crossing, in one of the two positions above.
WHAT YOU'VE LEARNED
A quick recap of today's lesson.
Two parallel lines, one line across them, and the angles that always match.
What you need to know
- A transversal is a line that crosses two or more other lines.
- Alternate angles are between the two lines, on opposite sides of the transversal, one at each crossing. On parallel lines, alternate angles are equal.
- Corresponding angles are in the same position at each crossing, for example above the line and right of the transversal both times. On parallel lines, corresponding angles are equal.
- Give the reason with the correct name: 'alternate angles are equal' or 'corresponding angles are equal'.
The big picture
A transversal is a line that crosses two other lines, making four angles at each crossing. Alternate angles are between the two lines, on opposite sides of the transversal. Corresponding angles are in the same position at each crossing. When the two lines are parallel, alternate angles are equal and corresponding angles are equal. When you use either fact, write the reason with its correct name: 'alternate angles are equal' or 'corresponding angles are equal'.
Key points
Worked example
Problem
JK and LM are parallel lines, with J and L on the left. A transversal meets JK at S and LM at T, with S higher up. ∠KST = (3x − 20)° and ∠STL = (2x + 15)°. Find the size of each angle, and state the reason you used.
⚠ Watch out
Mixing up the two names. A pair of angles that are both between the lines, on opposite sides of the transversal, is alternate, not corresponding. The size can still come out right, but a reason that gives the wrong name for the pair is a wrong reason.
Memory hook
Between and across: alternate. Same seat at the next crossing: corresponding. Both are equal, but only on parallel lines.
Check yourself
EF crosses parallel lines AB and CD at P and Q (A and C on the left, E above AB). ∠APE = 57°. Which angle at Q corresponds to ∠APE? Check: ∠CQP, also 57°.
Flashcards
(6)What is a transversal?
Where do alternate angles sit?
Where do corresponding angles sit?
When are alternate angles equal, and when are corresponding angles equal?
How do you write the reason when you use an alternate pair?
Why are corresponding angles on parallel lines equal?
Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.
Learning with Lightbulb is opening soon
You can use this lesson now. Join the waitlist and we'll let you know when the full Lightbulb experience is ready.
Keep me postedMore AQA GCSE Maths topics
- 3D shapes — properties of faces, surfaces, edges, vertices
- Angle properties at a point and on a line
- Angle sum in a triangle and polygons
- Approximate solutions of equations from a graph
- Approximate solutions of quadratics from a graph
- Arc lengths, angles and sector areas
- Area and volume formulae — triangles, parallelograms, trapezia, prisms, cylinders
- Box plots, quartiles, inter-quartile range (Higher)
- Calculate with roots and integer indices
- Circle definitions and properties
- Combinations of transformations and invariance (Higher)
- Compare distributions — graphical and central tendency/spread
How this lesson was checked. This AQA GCSE Maths (specification 8300)lesson was published through Lightbulb Learning's human-designed editorial process — the educational standards, accuracy rules and publication checks it must pass were authored and approved by Philip Halpin. It passed subject-specific assessment, automated educational checks and technical publication verification before going live (publication checks completed 24 September 2026). Published pages are monitored, human spot-checking is ongoing across the lesson library, and anything found wrong is corrected or withdrawn. How our lessons are made and checked. Spotted a mistake? Email hello@lightbulblearning.co and we'll review it.