In you think of the two heart shapes?

In this lesson, you will find out how you can tell if two things are congruent or not. You will also see simple and more complex examples of congruency.

Congruent Defined

When two things are said to be congruent, it means that all of their measurements are identical. A square that has sides measuring 4 inches will be congruent to another square that also has 4-inch sides. Even if the other square is placed in a different place or flipped around, the two squares are still congruent to each other.

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Congruency Symbol

Congruency symbol.
Are these two shapes congruent?
congruent

Look at the two blue shapes. Are these congruent? Let’s go through our two-step check for congruency.

  • First, are these two shapes the same type? Well, the first looks like a sideways dome and the second looks like an upright dome. So, yes, they are the same type – they are both dome shapes.
  • Second, do these have the same measurements? We need to measure the identifying measurements of the shape. For this dome shape, we need the height and the width.

    Let’s take out a ruler and measure them. Measuring them, we see that yes indeed, their measurements are the same. So, we can say confidently that these two shapes are congruent.

What about these shapes?
congruent

Let’s try another example.

What do you think of the two heart shapes? Are they congruent? Let’s go through our two-step check process before we answer.

  • First, are these two shapes of the same type? They both look like hearts – so yes, they are of the same type.
  • Next, are they the same size? Getting out our ruler, we start measuring the height of the first heart. When we measure the height of the second heart, we notice that it is smaller. Do we need to continue measuring the width? No, because we just realized that they are not the same size. Because they are not the same size, they are not congruent.

Lesson Summary

For two shapes to be congruent, it means that all of their measurements are identical. The symbol for congruency is an equal sign with a squiggly on top. The check for congruency is a two-step process involving checking for the same type of shape and then checking to see if they are the same size with the same measurements.

If both steps yield a positive answer, then the two shapes are congruent.

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