# Understanding Congruent Shapes Worksheets

This section sets the stage for geometric proofs. Congruence is a relationship between shapes. When two geometric shapes are congruent everything about them is identical. This means that one can be considered to be the other. If you are able to determine the length of a side of one of the figures in a congruent relationship, you also determined that measure in the other shape. This is the same as angles whether they are interior or exterior in position. We can use these reference points to learn a great deal about any shapes found within a coordinate system or free flowing if they are contact with other shapes. These lessons and worksheets will help students recognize shapes that are congruent and use that to their advantage.

### Aligned Standard: 8.G.A.2

- Congruent? Step-by-Step Lesson- We look at shape turns and make up our mind from that.
- Guided Lesson - Don't get tricked on number 2.
- Guided Lesson Explanation - These are some of the simplest explanations I have written for the whole site.
- Recognizing Similar and Congruent Figures 5 Pack - An easy check it off activity.
- Practice Worksheet - "C" for congruent and "N" for non congruent.
- Matching Worksheet - Make sure that you are aware that the colors in the answers are changed on purpose.
- Identifying Congruent Figures Lesson and Practice - Which is congruent to the first image?
- Congruent Versus Similar Worksheet - What is similar you ask? Exactly; just not congruent.
- Stating Similarity or Congruency Lesson and Practice - A quick refresher lesson for you and a bunch of practice.
- Who is Similar? Worksheet - Find a similar shape to the first one.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Color adds a bit more difficulty to this skill and helps you really understand where the kids are at.

- Homework 1 - Congruent means that two shapes exactly match. These shapes have the same sizes and shapes, even though their orientations may differ.
- Homework 2 - These two shapes are not same. So, that would mean that these shapes are non-congruent.
- Homework 3 - Triangles and a whole mess more shapes to run through.

### Practice Worksheets

Many teachers tell me that these make great smart board class quizzes and review sheets.

- Practice 1 - Are these figures congruent? You will see all types of objects to classify.
- Practice 2 - It would also indicate that the shapes have the same sizes and shapes, even though their orientations may differ.
- Practice 3 - You can move congruent shapes in any direction; they will still be congruent.

### Math Skill Quizzes

I'm working on a set of black and white quizzes for this now.

- Quiz 1 - Black and white. This leads you right into the concept of symmetry.
- Quiz 2 - Color brings these objects to life for you to evaluate.
- Quiz 3 - The shapes are similar in appearance, but the shape on the right is much larger and thicker. This would indicate that they are non congruent.

### What Are Congruent Shapes?

Have you ever seen identical twins? That's right! They are strikingly similar. Every feature, their hair, eyes, noses, hands, everything is absolutely the same. Just like humans have identical twins, the mathematical term for identical twins is "congruent." These shapes are exactly like each. Let's say that you have a triangular object in your hand. Now place the object in front of a mirror. The reflection that you see will be known as 'congruent' to the original triangular piece. Every side is the same length and all angles are equal measures.

When the objects are said to be congruent, the shape, corresponding sides, and angles are also the same. Let us take an example. On a blank page, draw a rectangle with sides of 5 cm and 6 cm. Below it, draw another rectangle with similar measurements. These rectangles are now congruent with one another. You can see two congruent rectangles, not to those measures, found to the right. All other image relationships are like comparing apples to oranges.

You may also run into a comparison between geometric shapes when they have the same size but are not identical. Figures that have the same shape but are not exactly the same are called similar.

### Why Is This Topic Important in The Real World?

The world of architecture and construction is absolutely infatuated with congruent shapes to support most major facets of modern infrastructure. Due to the fact that they are essentially equivalent in all dimensions they create strong and consistent reinforcers for foundations, buildings, and bridges. The level of consistency that is created allows the structure to be equally stable when confronted with weather and winds. If look at most modern buildings, they entirely composed of congruent shapes inside and out of the structure itself. This includes the foundation to the metal skeleton frame to even the safety features. If you look at the fire escapes of most apartment buildings, you will see this evident too. You will see this present in nature. Most leaves of plants and trees exhibit a level symmetry that also reflects this as well. My favorite way to display this is the good ole' monkey bars on the playground. If you take a walk out to your favorite play yard and mentally cut the monkey bars down the middle, you will basically see a mirrored shape composition on the half that is missing. This is a great activity to show students if you have one available to view.