Lesson video

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Hello, my name is Mr.Claper.

And today, we're going to be looking at angles and parallel lines with one transversal.

Let's begin by looking at this diagram.

We have two straight lines intersecting each other, which means we have two pairs of equal angles as they are vertically opposite, one another.

If I duplicate this diagram and place it on top of the original diagram, we have a pair of parallel lines.

Now, what we're going to be looking at are relationships between angles and parallel lines with one transversal.

A transversal is a diagonal line, which intersects two or more parallel lines.

Let's take a look at this example.

Here is a set of parallel lines and the transversal.

Looking at this diagram, these two angles must be equal.

And we can see this from our original diagram in the box to the right.

These two angles will always be equal.

These two angles will also always be equal.

If we have two angles, which are on the same side of the transversal, and they're are both, either are both, or below the parallel lines, then these angles are said to be corresponding, and corresponding angles are always equal.

Let's have a look at another relationship.

From the figure to the right, we can see that these two angles must be equal.

And these two angles must also be equal.

This is because these angles are said to be alternate.

Alternate angles are both inside a pair of parallel lines, and they appear on either side of a transversal.

Alternate angles are always equal.

Let's take our original diagram one more time.

If I place a parallelogram on top of this diagram, and highlight these two angles, we can see that these two angles are not equal.

One of the angles is acute, and one of the angles is obtuse.

These angles are known to be co-interior, and co-interior angles have a sum of 180 degrees.

We can identify co-interior angles as reside in between our two parallel lines, and they are also on the same side of a transversal.

Co-interior angles have a sum of 180 degrees, this is a fact that we need to remember.

Here are some questions for you to try.

Pause the video to complete your task, and click resume once you're finished.

So if you struggle with these questions, you might want to go back and take some notes.

So we know that corresponding angles must be on the same side of a transversal, and they must both be either above or below our parallel lines.

Alternate angles are on either side of a transversal and they reside inside our parallel lines.

And co-interior angles are both inside our parallel lines, and on the same side of our transversal.

Let's take a look at this example.

We need to find the size of angle A.

In the diagram, our two parallel lines are here, and we have a one transversal.

Looking at the two angles given, they are both above each of the parallel lines, and they reside on the same side of our transversal.

These two angles are corresponding, and corresponding angles are equal, therefore, the value of A must be 78 degrees.

Let's have a look at this example.

Again, we have our two parallel lines.

Looking our two angles, they both reside on the same side of our transversal.

However, both angles are inside our parallel lines.

These two angles are co-interior, and co-interior angles have a sum of 180 degrees.

Therefore, A must be 102 degrees, as A plus 78 must give us 180 degrees in total.

Here are some questions for you to try.

Pause the video to complete your task, and click resume once you're finished.

So again, just think carefully about each rule.

So the first example, these two angles are alternate, and alternate angles are always equal.

And for the second example at the top right, these angles are corresponding and therefore, they are also equal.

If you look at the bottom left, these are co-interior, so they must have a sum of 180.

And if we look carefully, they can not be equal as one of them is obtuse and the other is acute.

And our last example is another example of corresponding angles, so they, again, must be equal.

Let's take a look at this example.

This example is a little bit more tricky as we can't just use one of our three rules that we've learned.

In lots of cases, you will encounter questions where you might need to find more than one angle to help you find your final answer.

Let's take a look at this one.

What I could do is find another angle in the problem.

So I could say that I've got two parallel lines, and the angle opposite 63 degrees must be equal as they're vertically opposites.

And as this angle is 63 degrees, if I compare my new 63 degree angle with A, these two angles are co-interior, therefore, they must have a sum of 180, and therefore, A must be 117 degrees.

Let's try another way to solve the same problem.

I have my two parallel lines, and if I look carefully at my transversal, all of the angles on my transversal must be equal to 180 degrees, as the angles on a straight line have a sum of 180 degrees.

That means that this angle must be 117 degrees.

Now, looking at our new 117 degree angle, and comparing it to our angle A, these two angles are alternate.

Therefore, they must be equal, and therefore, A must be 117.

There are many ways that you can solve problems like this.

You just need to find one that will suit you.

Here are some questions for you to try.

Pause the video to complete your task, and click resume once you're finished.

So let's take a look at question three.

So we're trying to decide if AB and CD are parallel.

Well, it looks as though we have two co-interior angles, but we should know that co-interior angles must have a sum of 180 degrees.

However, if we add our two angles together, we do not have a sum of 180 degrees, we actually get 178 degrees.

Therefore, AB and CD cannot be parallel.

And if we take a look at question four, we need to work in steps.

So you may need to find other angles in this diagram before getting to the conclusion that P must be equal to 87.

So just be careful with that one.

There's many ways to solve that problem.

And here is your last question.

Pause the video to complete your task, and click resume once you're finished.

And here is the solution.

So we're trying to decide if Mo's statement is correct, and we should establish that Mo is not correct.

This is because our two parallel lines have been highlighted in our question.

So the two angles which would have a sum of 180 would be our 73 degree angle, and the angle D.

So therefore, the angle D would actually be 107 degrees, not 108 degrees.

And that ties up our lesson.

I hope enjoyed finding angles and parallel lines.

Why not try the next lesson, which is angles and parallel lines with two transversals.