The Secrets to Congruent Shapes and Figures
Get the free Congruent Shapes worksheet and other resources for teaching & understanding Congruent Shapes
Here’s How to Identify Congruent Shapes
Congruent Shapes are figures that have the same shape and the same size. Congruent Shapes also have equal side lengths and equal angle measures. You can determine if two shapes are Congruent by following a series of transformations that will prove that they are congruent. Transformations can include translations, reflections, and rotations. You can always double check to make sure that the figures are Congruent Shapes by ensuring that they are identical once they ar transformed.
Common Core Standard: 8.G.C
The Answer to: What does Congruent mean in Math?
So what is a congruent shape anyway? Congruent Shapes are shapes that have a similar shape and a similar size. Congruent Figures have equivalent side lengths and equivalent angle measures. You can decide whether shapes are congruent by following a series of changes that will demonstrate that they are congruent. You can check to see if shapes are congruent by using incorporate transformations, reflections, and rotations.
3 Simple Steps for Identifying Congruent Figures
- You have to match the original shape up to the shape that has been transformed.
- To prove that they are the same shape you can use either translations, reflections, and rotations.
- You must check each shape to make sure it is lined up once you are done.
Congruent Shapes Practice Problems Quiz
Watch the Congruent Figures, Congruent Shapes, and Congruent Angles Examples Video Explanation
Watch our free video on how to solve Congruent Shapes. This video shows how to solve problems that are on our free Congruent Shapes worksheets that you can get by submitting your email above.
Watch the free Congruent Figures video on YouTube here: Congruent Shapes Video
This video is about the congruent shapes definition. You can get the similar and congruent figures worksheet used in this video for free by clicking on the link in the description below.
In talking about congruent shapes you have to understand that congruent shapes mean that the shapes have to be identical. This means that they have the same size and shape.
Problem one gives us two examples of congruent shapes with triangles. These triangles look like they are the same size and shape even though the orientation is different. Even though the triangles are rotated, it looks like this has been spun or spun over, they look like they are the same exact size and the same exact shape. Because of this they are congruent.
Our second problem gives us two rectangles the rectangles are the same shape but they are different sizes. This one is obviously bigger than this one so this would not be congruent. Number 3, same thing. We have two arrows pointing straight up they are the same shape but they are different sizes. They are also not congruent.
The second part of our congruent shape worksheet asks us to describe the sequence of transformations that result in the transformation from figure a to figure a prime. Now when they say a sequence of transformations what they’re referring to is either translation, rotations, or reflections. When it says describe the sequence of transformations, what they want you to do is to look at figure a and explain in terms of translations, rotations, and reflections, how you move from shape a to a prime.
Looking at the first problem in the second part of our congruent shapes worksheet, we have figure a here, which I’m going to outline in red, and you have to get it to figure a prime, which is over here which I’m going to use blue for. In order to go from one to the other you have to use either rotation, reflection, or a translation. We can eliminate a couple of those just by looking at this problem. A translation is a slide which means the whole shape would slide either left or right or up or down. And you can tell if you slide this it’s not going to line up. We can go ahead and eliminate translation.
The easiest way to transform this from this shape into this shape is to reflect across the Y axis. If we take our figure and we reflect across the Y axis all the points will line up. In order to double check this we can count how many spaces away from the y axis each point is. This is three so if you go in this direction that is also three. And then down bottom we’re going to count three over and then if you go this way I count three over and it’s here. This is eight away and then this will also be eight away and then this will also line up with this over here. We can use a reflection across the y-axis to translate our figure a into a prime. The solution for this first problem is that we have to reflect over the y-axis and is a congruent shapes examples.
Problem three gives us two triangles. Now we have to ask ourselves what are congruent shapes before transforming figure a into figure a Prime. We can go ahead and outline a in red. You can see it better if we were to translate this straight up. This would not work because we have to flip the shape around has to be spun.
What we’re going to do is we’re going to reflect across the x-axis this time so that we change the orientation of the shape. We’ll reflect and when we reflect we’re going to count the spaces away from the x-axis each point is or each vertices. This will be one two three four five six so you go now this time when we draw our triangle. It does not line up perfectly with our new figure so we still have to move it one more time.
What we’re going to do is we’re going to take our shape and we’re going to move it to the right two and then down one. Each vertices will go right to and then down one and then right two and then down one. Our new and final shape will be here. Our solution will be we first have to reflect across the x-axis and then translate x + 2 y -1 because we went right 2 and then down 1 and that’s our solution. Hopefully this help you understand what is a congruent figure and you can try these practice problems on the free congruent figures worksheets above.
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