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Understanding Congruent Shapes

8.G.A.2
Answer Keys Here

Aligned To Common Core Standard:

Grade 8 Geometry - 8.G.A.2

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 shapes." 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. 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 5cm and 6 cm. Below it, draw another rectangle with similar measurements. These rectangles are now congruent with one another. These lessons and worksheets will help students recognize shapes that are congruent and use that to their advantage.

Printable Worksheets And Lessons




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.


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.