# Congruent Shapes

Hey, guys! Welcome to this video on congruent objects.

What happens when I take this object,

and I flip it?

It looks pretty different, right? But aren’t all the sides still the same? If I flip it back, we can clearly see that the two objects are the same.

This is what we call congruent objects – shapes that can be flipped, turned, slid to make the same shape. All the sides of each shape must be identical.

There are a few different ways you can move congruent objects. Moving the object using one of these three movements may change the position or the way that the shape looks, but the shape itself will always remain the same.

The first movement we will talk about is a rotation. One way you can move a congruent shape is by turning it, or rotating it.

The second movement is a reflection. A reflection happens when an object is flipped across an imaginary line, or axis. It’s almost as if the object is looking at itself in the mirror.

The third, and final, movement is a translation. A translation happens when you move a shape by just simply sliding it in any direction. So you are not turning it or flipping it, you are just sliding it.

Okay, now it’s time to take a look.

The two triangles above are congruent, but they have been flipped across the y-axis. So, this is a reflection. It is still the exact same triangle, the only difference is that it has been flipped.

The two triangles above are congruent as well, but they have been rotated, or turned.

The two arrows above are identical in shape and in size, so we know that they are congruent. However, they have been slid upward. This movement is a translation.

Okay, now it’s your turn to practice.

Identify if the following shapes are congruent or not. If they’re congruent, then identify how they have been moved—by reflection, rotation, or translation.

Are these two shapes congruent?

No, they’re not congruent. We can see that they are different sizes, and one star has six points while the other one has five. To see this more clearly, we can place them on top of one another.

Are these two shapes congruent?

Yeah! We can see that they are identical; however, they have been moved. What type of movement is this? Well, it looks like they were just flipped, right? If we imagine that there is a line through the middle, we can see that they have been flipped across the line. This shape has been reflected.

Are these two shapes congruent?

No. We can see that they are different sizes by placing them on top of one another.

Okay, last one. Are these two shapes congruent?

Yeah! They are identical in shape and size, but what type of movement has been made? Was it flipped like the last one? No. It’s not a reflection. Has it been turned or rotated? No, so it’s not a rotation. Has it been slid? Yes, so we know that this is a translation.

## Practice Questions

Question #1:

Which statement is true?

Congruent figures have different sides and angles.

Congruent figures are the same size but not the same shape.

Congruent figures are the same shape but not the same size.

Congruent figures are the same size and shape.

Congruent figures have the exact same size and shape. Even when reflected, rotated, or translated, their size and shape remain identical.

Question #2:

Identify the type of transformation shown in the two congruent shapes below:

Rotation

Reflection

Translation

Dilation

Triangle EFG is reflected across the x-axis so that one triangle shows a mirror image of the other. Therefore, this is an example of a reflection.

Question #3:

Which type of transformation moves a figure by sliding it vertically, horizontally, or both?

Dilation

Reflection

Rotation

Translation

A translation happens when a congruent shape slides to another position without being rotated or flipped. The congruent shape can be translated vertically and horizontally.

Question #4:

Caleb works at an art museum and is in charge of a new sculpture installation. He proposes a location for the sculpture and presents it to his boss. Caleb’s boss wants the sculpture turned to the left, as shown in the image below. What type of transformation is this?

Reflection

Translation

Rotation

Dilation

When a congruent shape is turned, it’s rotated about a fixed point. The L-shaped sculpture is turned counter-clockwise to a new position. Therefore, the transformation taking place is rotation.

Question #5:

Janelle used a ruler to trace a line on a piece of graph paper. Her line was five units long. Then, she slid her ruler down eight units and traced another line on the graph paper. This line was also five units long. What type of transformation did Janelle perform?

Translation

Dilation

Rotation

Reflection

A translation happens when a figure is moved from one location to another by sliding it in a horizontal or vertical direction. The size and shape of the figure remain the same. Since Janelle slid her ruler eight units down and created a line identical to her original line, she performed a translation.