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Identify Corresponding Angles

In this worksheet, students will learn how to recognise corresponding angles and use the key fact, that corresponding angles are equal, to find the value of unknown angles and solve related problems.

'Identify Corresponding Angles' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Geometry and Measures, Basic Geometry

Curriculum subtopic:   Properties and Constructions, Angles

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

There are lots of different angles to be found between parallel lines.

 

Here we are going to look at corresponding angles.

We find them in parallel lines on the same side of the transversal (the line that goes through the middle of the parallel lines).

 

Review the two diagrams below showing corresponding angles:

 

Diagrams showing examples of corresponding angles

 

As we can see in the diagrams above, corresponding angles sit either below or above the parallel lines.

 

They also look like the letter F.

 

We could also say that they are in matching corners, so the word 'corresponding' can be linked to 'corners'. 

 

The really hard part is spotting corresponding angles in diagrams.

 

Once we find them, we can apply the rule that these angles are always equal

 

 

 

Girl with a magnifying glass

 

Right then, let's get investigating now. 

 

In this activity, we will learn how to recognise corresponding angles and use the key fact, that corresponding angles are equal, to find the value of unknown angles and solve related problems. 

Explore the unknown angles on the diagram below labelled with letters:

Diagrams showing a number of unknown angles expressed as letters

Which pair of angles are corresponding?

d and e

e and a

c and e

e and b

Observe the known and unknown angles on the diagram below:

Diagrams showing a number of known and unknown angles highlighted in yellow

Now type a letter then a number to complete the statements below. 

d and e

e and a

c and e

e and b

Explore the known and unknown angles on the diagram below:

Diagrams showing a number of known and unknown angles

Then select the correct answers to complete the statements below. 

 

 xy108°72°
The corresponding angle to 72°...
The value of the angle is...

Review the collection of diagrams below:

 

A collection of six diagrams showing angles created within parallel lines

 

Which diagrams show examples of corresponding angles?

a)

b)

c)

d)

e)

f)

Explore the unknown angles on the diagram below labelled with letters:

Diagrams showing a number of unknown angles expressed as letters

Which pairs of angles are corresponding which each other?

h and a

g and b

g and d

e and d

e and a

f and c

Next, investigate the unknown angles on the diagram below:

Diagrams showing a number of unknown angles expressed as letters

Now type a letter then a word to complete the statements below. 

h and a

g and b

g and d

e and d

e and a

f and c

Now review this new diagram:

Diagrams showing a number of unknown angles expressed as letters

Which angle corresponds with g?

a

b

c

d

Observe the known and unknown angles on the diagram below:

Diagrams showing a number of known and unknown angles

Which pairs of angles are corresponding?

y and 72°

x and 72°

y and 148°

x and 148°

Review the known and unknown angles on this new diagram:

 

Diagrams showing a number of known and unknown angles

 

Then select the correct answers to complete the expressions below. 

 132°48°
Angle a =
Angle b =

Investigate the known and unknown angles on this final diagram now:

Diagrams showing a number of known and unknown angles

What is the value of angle x?

 132°48°
Angle a =
Angle b =
  • Question 1

Explore the unknown angles on the diagram below labelled with letters:

Diagrams showing a number of unknown angles expressed as letters

Which pair of angles are corresponding?

CORRECT ANSWER
d and e
EDDIE SAYS
Sometimes these angles can be tricky to spot if there are several shown in a collection. Consider each pair one at a time, ignoring all other angles in each case. Remember we are looking for two angles which are on the same side of the transversal and both sitting either above or below the parallel lines, or in an F-shape. The only pair which show this accurately are d and e. Review the Introduction now before you move on if any of these terms are unfamiliar or you found recognising this pair of corresponding angles to be tricky.
  • Question 2

Observe the known and unknown angles on the diagram below:

Diagrams showing a number of known and unknown angles highlighted in yellow

Now type a letter then a number to complete the statements below. 

CORRECT ANSWER
EDDIE SAYS
All our angles are on the same side of the transversal here, so we just need to work out which angle is in the same location as 130° but just attached to the upper parallel line instead. The angle which is in this same position above is angle y, and it has exactly the same value as its partner.
  • Question 3

Explore the known and unknown angles on the diagram below:

Diagrams showing a number of known and unknown angles

Then select the correct answers to complete the statements below. 

 

CORRECT ANSWER
 xy108°72°
The corresponding angle to 72°...
The value of the angle is...
EDDIE SAYS
Our 72° starting point is sitting to the left of the transversal and above the upper parallel line. The angle in the same location in relation to the lower parallel line is angle x, and this pair of angles have the same value.
  • Question 4

Review the collection of diagrams below:

 

A collection of six diagrams showing angles created within parallel lines

 

Which diagrams show examples of corresponding angles?

CORRECT ANSWER
b)
f)
EDDIE SAYS
Did you spot these corresponding angles quite quickly? We can use the key clue from the Introduction - can you see any F-shapes with both angles in the same locations on the upper and lower parallel lines? Diagram b) shows two angles on the left of the transversal, positioned in the same place, so this is an example of a corresponding angle. Diagram f) is a little trickier to work out, as there are four angles shown here. Angle Z and 32° may look like they are corresponding, but they are actually on opposite sides of the parallel lines. It is angle X and angle y which are in fact corresponding, as they are on the same side of the transversal and both to the right of the parallel lines. Did you spot that?
  • Question 5

Explore the unknown angles on the diagram below labelled with letters:

Diagrams showing a number of unknown angles expressed as letters

Which pairs of angles are corresponding which each other?

CORRECT ANSWER
h and a
g and b
e and d
f and c
EDDIE SAYS
It sure makes our eyes boggle to look at so many angles in one go! Just take your time... Look on the same side of the transversal for our matches and look for angles in the same corners, either both above or below the parallel lines. Were you able to identify the four viable pairs showing corresponding angles?
  • Question 6

Next, investigate the unknown angles on the diagram below:

Diagrams showing a number of unknown angles expressed as letters

Now type a letter then a word to complete the statements below. 

CORRECT ANSWER
EDDIE SAYS
Let's start at angle h, stay on the same side of the central line, jump down to the same point on the parallel line below and, hey presto, we are there! So angle a is alternate and has the same value as angle h. Quite often, we will be asked to explain our answer, so the justification we can use is simply: "Corresponding angles are always equal."
  • Question 7

Now review this new diagram:

Diagrams showing a number of unknown angles expressed as letters

Which angle corresponds with g?

CORRECT ANSWER
b
EDDIE SAYS
Hopefully this is becoming really familiar now. Same side, same corner... Angle g is our starting point. We know that the corresponding angle to g will be on the same side of the transversal and below each of the parallel lines. So the corresponding angle could only be b. Can you see the F-shape which has angles g and b in its corners?
  • Question 8

Observe the known and unknown angles on the diagram below:

Diagrams showing a number of known and unknown angles

Which pairs of angles are corresponding?

CORRECT ANSWER
y and 148°
EDDIE SAYS
How can one extra line confuse things so much?! Remember corresponding angles are always within pairs of parallel lines, so this is where we can look first. We can see two possible F-shapes: One created using the parallel lines with a diagonal transversal; And one create using the parallel lines with a horizontal transversal. The corresponding angle to x and 72° in the diagonal F have not been provided, so these can be ruled out. The corresponding angle to y is 148° in the horizontal F, but you will need to look closely and disregard the other angles and lines to spot this. How did you get on?
  • Question 9

Review the known and unknown angles on this new diagram:

 

Diagrams showing a number of known and unknown angles

 

Then select the correct answers to complete the expressions below. 

CORRECT ANSWER
 132°48°
Angle a =
Angle b =
EDDIE SAYS
Corresponding angles are on the same side of the transversal and we know they have the same value. A helpful way of thinking about 'corresponding' angles, is that they are on the same side as they 'agree'. 'Corresponding' can also mean equivalent or the same, so we can think of them as being in the same place, just one line up/down. So angle a is agreeing with 48°, whilst angle b is in the same place, just one row down, as 132°.
  • Question 10

Investigate the known and unknown angles on this final diagram now:

Diagrams showing a number of known and unknown angles

What is the value of angle x?

CORRECT ANSWER
EDDIE SAYS
Oh no, this is not fair is it?! Actually this question is much easier than it appears at first glance. Examiners like to sneak this sort of thing in to check we haven't fallen asleep, so wakey, wakey! We know that angles on a straight line add up to 180°. So we can take 56° away from 180° and this will give us the corresponding angle to x. We know that corresponding angles are the same so once we have this value, we also know the value of x - happy days! Well done! In this activity you have learnt how to recognise corresponding angles and use the key fact, that corresponding angles are equal, to find the value of unknown angles and solve related problems.
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