Lesson video

Hi, I'm Mr Chan.

And in this lesson, we're going to learn how to identify congruent shapes.

What does it mean for shapes to be congruent? So what does congruent mean? Well, shapes are congruent, when all their sides on their angles are equal to each other.

So, what I mean by that is, they're identical in shape and size, but could be in a different orientation.

So let's have a look at an example of what I mean by that.

I've got a triangle here, I could make an identical copy to that, and I could say those two shifts are congruent.

Now it doesn't matter if I rotate this triangle, into a different orientation, they would still remain congruent to each other.

Here's a question for you to try.

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

Here are the answers.

So when we're looking for congruent shapes, we're looking for shapes that are identical in the shape and size, but then maybe rotated in into a different orientation.

So the pairs that we do gets are shown on that, A and D, B and C, F and G.

There's a few ways that we can tell if two triangles are congruent, and we call these the conditions for congruency.

So let's take them one at a time.

The first condition we can test, if a triangle is congruent to each other, is whether the two triangles have equal sides.

So we call this the side, side, side relationship, where the two triangles are congruent, if all three sides are the same length in each triangle.

Another condition for congruency would be, side, angle, side.

So we have one side equal to the same side in the triangle, then an angle that's equal, and then a side that equal.

So two triangles are congruent, if two sides and the angle between those two sides are equal.

There are a couple of other ways we can tell if two triangles are congruent, another one would be looking for whether they're both right angle triangles, that have the same hypotenuse length, and one other side that's equal to each other.

So we call this the right-angle, hypotenuse, side condition, where we're looking for two right-angle triangles, where the hypotenuse and one sideline are equal.

Another one would be, well, we have an angle that's equal in the triangles, along with a side, followed by another angle in that order.

So two triangles are congruent where two angles and the side between them are equal as well.

So here's a bit of a question where we're asked, why isn't angle, angle, angle condition for congruency? So where the pairs of angles in both triangles are equal to each other, why wouldn't that mean, that the two triangles are congruent, or identical to each other? So, if we remember in a previous lesson, we learned about similar shapes and similar triangles, we learned that similar shapes, are where one triangle is an enlargement of another triangle, now we also learned that, when we enlarge a shape, the angles remain the same.

So if we've enlarged shape, that would mean that they're not congruent, they're not identical to each other.

So, just knowing that all three angles are equal to each other, isn't enough to know whether the shapes are congruent or not.

All that means is that they are similar.

So here is a recap conditions of congruency that we've covered in this lesson.

Where we have two triangles, that have side, side side, all equal to each other, where we have two triangles, that are right-angled and the hypotenuse and one of the side lengths are equal to each other, where we have a side, angle, and then another side, so the angle between two sides, are all equal to each other.

And finally, angle, side, angle, where we have an angle with a side, and then followed by another angle.

Let's have a look at an example.

In this question, we're asked, are these triangles congruent and explain why? So I can see we've got two triangles, one triangle on the left has 10 centimetres, 15 centimetres, and 7.

5 centimetre side-lengths.

And in my triangle on the right, I also do have 10 centimetres, 15 centimetres, and 7.

5 centimetres.

All the three sides being equal to each other, I can say, yes, those two triangles are congruent, because all the three sides are equal in length.

The condition for congruency, there would be side, side, side.

Here's some questions for you to try.

Pause the video as you complete the task, resume the video once you're finished.

Here are the answers for question two.

If you found it difficult to explain why these triangles were congruent, then it might be worth recapping some of the examples, for the conditions of congruency, earlier in the lesson.

Here's some more questions for you to try.

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

Here are the answers.

Remember that congruency doesn't rely upon orientation.

So if it helps you, draw the triangles out separately, and then rotate them so that they're in the same orientation to help you decide, whether the triangles are congruent or not.

Here's another question you can try.

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

Now, this question links into another topic in maths, called transformations.

So when you learn about transformations, you will learn that rotations and reflections don't actually change the size of the shape.

So if this shape hasn't been changed in the terms of the size, that means the ship will remain congruent.

That's all for this lesson, thanks for watching.