New
New
Year 8

Corresponding angles

I can recognise that a pair of parallel lines traversed by a straight line produces equal corresponding angles.

New
New
Year 8

Corresponding angles

I can recognise that a pair of parallel lines traversed by a straight line produces equal corresponding angles.

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Lesson details

Key learning points

  1. The different arrangements of 3 line segments can be described and categorised.
  2. One of these arrangements involves a transversal.
  3. Corresponding angles can be identified in this arrangement.
  4. If the lines cut by the transversal are parallel these corresponding angles are equal.
  5. Knowledge of corresponding angles can be used to find unknown angles.

Keywords

  • Corresponding angles - Corresponding angles are a pair of angles at different vertices on the same side of a transversal in equivalent positions.

  • Transversal - A transversal is any ٭line that intersects two or more ٭lines at distinct (different) points. (٭line, line segment or ray)

Common misconception

Transversals must intersect a pair of parallel lines.

Transversals can intersect any set of lines or line segments, no matter whether any of those lines or line segments are parallel or not.

It is important to emphasise the quality of a student's explanation when justifying the size of an angle. "Corresponding angles are equal" can be more accurately worded as "corresponding angles on a pair of parallel lines are equal".
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).

Lesson video

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6 Questions

Q1.
TU is a straight line segment. Find the size of angle $$a$$, in degrees.
An image in a quiz
Correct Answer: 34, 34°, 34 degrees, 34degrees
Q2.
This diagram shows two intersecting line segments. Match each angle or justification for the size of angles $$b$$° and $$c$$° to the correct value or statement.
An image in a quiz
Correct Answer:size of angle $$\text{ }b$$°,162°

162°

Correct Answer:size of angle $$\text{ }c$$°,18°

18°

Correct Answer:justification for angle $$b$$°,angles about a point on a straight line sum to 180°

angles about a point on a straight line sum to 180°

Correct Answer:justification for angle $$c$$°,vertically opposite angles are equal

vertically opposite angles are equal

Correct Answer:not an angle on this diagram,36°

36°

Q3.
Match the line segment to the correct description that completes each sentence.
An image in a quiz
Correct Answer:AB,is parallel to IJ

is parallel to IJ

Correct Answer:CD,is parallel to GH

is parallel to GH

Correct Answer:KL,is not parallel to any other line segment in this diagram

is not parallel to any other line segment in this diagram

Q4.
Match each angle to its size.
An image in a quiz
Correct Answer:$$d$$°,110°

110°

Correct Answer:$$e$$°,70°

70°

Correct Answer:$$g$$°,38°

38°

Correct Answer:$$h$$°,104°

104°

Correct Answer:not an angle in this diagram,56°

56°

Q5.
AB, CD, and EF are all straight line segments. By first calculating the size of angles $$j$$° and $$k$$°, find the value of $$(j+k)$$°.
An image in a quiz
Correct Answer: 180, 180°
Q6.
Match each line segment to its correct description.
An image in a quiz
Correct Answer:AE,is parallel to CD

is parallel to CD

Correct Answer:AF,is parallel to BD

is parallel to BD

Correct Answer:BF,is perpendicular to CD

is perpendicular to CD

Correct Answer:AF,a longer line segment with a gradient of $$-\frac{1}{3}$$

a longer line segment with a gradient of $$-\frac{1}{3}$$

Correct Answer:BD,a shorter line segment with a gradient of $$-\frac{1}{3}$$

a shorter line segment with a gradient of $$-\frac{1}{3}$$

6 Questions

Q1.
Which of these statements is true for a transversal?
Correct answer: It is a line, a ray, or a line segment.
It must be a ray, as it can only extend infinitely in one direction.
Correct answer: It means to travel or lie across multiple things.
Correct answer: It is a line that lies across a group of other lines.
It means to intersect at a corresponding angle.
Q2.
Which of these line segments is a transversal?
An image in a quiz
AB
Correct answer: CD
EF
GH
They are all transversals to each other.
Q3.
Which angle is corresponding to angle $$\theta$$°?
An image in a quiz
$$a$$°
$$b$$°
Correct answer: $$c$$°
$$d$$°
Q4.
Which of these statements are correct for this diagram?
An image in a quiz
The transversal intersects two perpendicular line segments.
Correct answer: The transversal intersects two parallel line segments.
Angle $$x$$° = 66° because $$x$$° is parallel to 66°.
Correct answer: Angle $$x$$° = 66° because $$x$$° is corresponding to 66°.
Angle $$x$$° = 66° because $$x$$° is vertically opposite 66°.
Q5.
What is the size of angle $$x$$, in degrees?
An image in a quiz
Correct Answer: 131, 131°, 131 degrees, 131degrees
Q6.
Which angles are corresponding to $$\theta$$°?
An image in a quiz
$$a$$°
Correct answer: $$b$$°
$$c$$°
Correct answer: $$d$$°
$$e$$°