New
New
Year 10
Higher

Checking and securing understanding on chains of reasoning with angle facts

I can reason mathematically using my knowledge of angle facts.

New
New
Year 10
Higher

Checking and securing understanding on chains of reasoning with angle facts

I can reason mathematically using my knowledge of angle facts.

Lesson details

Key learning points

  1. Alternate, corresponding and co-interior angles can be identified in diagrams containing pairs of parallel lines.
  2. Facts about angles in parallel lines can be used to find unknown angles.
  3. 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.

There are often multiple ways to find the size of unknown angles. Pupils can be encouraged to find as many ways as they can to justify their answers using these different angle facts. They could also identify which angle facts would not be useful for each problem.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
is 65°. Use three letter angle notation.
An image in a quiz
Correct Answer: DAB, BAD
Q2.
Which angle is corresponding with ∠DBC?
An image in a quiz
∠BDG
∠EDB
Correct answer: ∠FDE
∠GDF
∠HBD
Q3.
Which angle is alternate with ∠DBC?
An image in a quiz
Correct answer: ∠BDG
∠EDB
∠FDE
∠GDF
∠HBD
Q4.
Which angle is co-interior with ∠DBC?
An image in a quiz
∠BDG
Correct answer: ∠EDB
∠FDE
∠GDF
∠HBD
Q5.
Which angle is vertically opposite with ∠DBC?
An image in a quiz
∠BDG
∠EDB
∠FDE
∠GDF
Correct answer: ∠HBA
Q6.
∠DBC = 89°. Which other angles in the image are also 89°?
An image in a quiz
Correct answer: ∠BDG
∠EDB
Correct answer: ∠FDE
∠GDF
Correct answer: ∠HBA

6 Questions

Q1.
Which angle fact can be used to justify why $$x=120$$ using a single statement?
An image in a quiz
Correct answer: 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.
Q2.
Which angle fact could be used to justify why $$x=120$$ using a single statement?
An image in a quiz
Alternate angles in parallel lines are equal.
Co-interior angles in parallel lines sum to 180°.
Correct answer: Corresponding angles in parallel lines are equal.
Vertically opposite angles are equal.
Q3.
The size of the angle marked $$x$$ is °.
An image in a quiz
Correct Answer: 299, two hundred and ninety nine
Q4.
The size of the angle marked $$x$$ is °.
An image in a quiz
Correct Answer: 52, fifty two
Q5.
The size of the angle marked $$x$$ is °.
An image in a quiz
Correct Answer: 75, seventy five
Q6.
The size of the angle marked $$x$$ is °.
An image in a quiz
Correct Answer: 105, one hundred and five