Checking and securing understanding on chains of reasoning with angle facts | Maths

Starter quiz

∠______ is 65°. Use three letter angle notation.

'DAB' ✓
Which angle is corresponding with ∠DBC?

∠BDG

∠EDB

∠FDE ✓

∠GDF

∠HBD
Which angle is alternate with ∠DBC?

∠BDG ✓

∠EDB

∠FDE

∠GDF

∠HBD
Which angle is co-interior with ∠DBC?

∠BDG

∠EDB ✓

∠FDE

∠GDF

∠HBD
Which angle is vertically opposite with ∠DBC?

∠BDG

∠EDB

∠FDE

∠GDF

∠HBA ✓
∠DBC = 89°. Which other angles in the image are also 89°?

∠BDG ✓

∠EDB

∠FDE ✓

∠GDF

∠HBA ✓

Exit quiz

Which angle fact can be used to justify why $x=120$ using a single statement?

Alternate angles in parallel lines are equal. ✓

Co-interior angles in parallel lines sum to 180°.

Corresponding angles in parallel lines are equal.

Vertically opposite angles are equal.
Which angle fact could be used to justify why $x=120$ using a single statement?

Alternate angles in parallel lines are equal.

Co-interior angles in parallel lines sum to 180°.

Corresponding angles in parallel lines are equal. ✓

Vertically opposite angles are equal.
The size of the angle marked $x$ is ______°.

'299' ✓
The size of the angle marked $x$ is ______°.

'52' ✓
The size of the angle marked $x$ is ______°.

'75' ✓
The size of the angle marked $x$ is ______°.

'105' ✓

Worksheet

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Lesson Details

Key learning points

Alternate, corresponding and co-interior angles can be identified in diagrams containing pairs of parallel lines.
Facts about angles in parallel lines can be used to find unknown angles.
Facts about angles in parallel lines can be used in succession to find multiple unknown angles.

Common misconception

Alternate angles are always equal to each other.

Alternate angles are equal when a transversal intersects parallel lines. If the transversal intersects a pair of lines that are not parallel then the alternate angles will not be equal.

Keywords

Corresponding angles - Corresponding angles are a pair of angles at different vertices on the same side of a transversal in equivalent positions.
Alternate angles - Alternate angles are a pair of angles both between or both outside two line segments that are on opposite sides of the transversal that cuts them.
Co-interior angles - Co-interior angles are on the same side of the transversal line and in between the two other line.