L3 · Comparing two angles: superimposing directly and indirectly; which is greater?

Learning goal

“I can compare two angles by superimposing - laying one on top of the other - and if the angles cannot be moved, I can compare each of them to the same third angle.”

Superimpose — to place one angle exactly on top of another angle to compare them.

Tracing — a copy of an angle, made on clear plastic or thin paper, that can be carried to another angle.

Greater angle — the angle with the wider opening.

Indirect comparison — comparing two angles by comparing each one to the same third angle, instead of to each other.

Worked example

Two angles are drawn on paper. Compare them by superimposing: Step 1: Place one angle on top of the other. Line up the two vertices exactly. Step 2: Line up one arm of each angle so they lie on top of each other. Step 3: Now look at the free arms. Angle B's free arm falls outside Angle A's free arm. Step 4: The angle whose free arm falls outside opens wider - Angle B is greater. (If the free arms match exactly, the angles are equal.) Say it plainly: vertices together, one arm together - then the free arms tell the story. Outside = greater; inside = less; matching = equal.

Check yourself — explain it

Superimposing works because...

Paired problem — example still visible

Two angles are superimposed. Angle P's free arm falls inside Angle Q's free arm. Which angle is greater? -> Angle Q

Faded completion — last step is yours

"Line up the ___ and one ___. The angle whose free arm falls ___ is the greater angle" -> vertices; arm; outside

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

Start practice →Take the unit quiz