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Two-dimensional Congruent Figures

8.G.A.2
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Aligned To Common Core Standard:

Grade 8 Geometry - 8.G.A.2

What are Two-dimensional Congruent Figures? You must have come across some identical twins, right? If not, let's understand what identical twins are. They are EXACTLY the same! From their eyes to their hair and every other body part, they are totally similar to each other. In math, we refer to this similarity as "Congruency." Just like identical twins, shapes and figures can be the same too. Let's say you drew a rectangle on one page of 6 cm length 5 cm height. On the next page, you drew another, slightly slant rectangle with the same measurements. These figures are now called congruent to each other. Hence when two figures are congruent, they have the same shape and the same size. Sometimes they may appear rotated or shifted, but all their sides are equal to each other. You will find that most designs are based on the concept of congruent shapes to help maintain a high level of structural integrity.

Printable Worksheets And Lessons






Homework Sheets

I made all different kinds of shapes on coordinate grids for you to enjoy.

  • Homework 1 - These figures are congruent since figure B is producedby translating each vertex of Figure A 4 to the right and 2 up.
  • Homework 2 - If it were a paper airplane, I would say that someone pushed it up. The figures are the same size, just moved. So, these figures are congruent since B was produced by translating each vertex of Figure B' 2 to the up and 6 right.
  • Homework 3 - If this were a triangular box, it would look as if the box fell on its right side or turned. In this figure, Figure B is a rotation of 90˚ of Fig A. So, the transformation is a rotation.



Practice Worksheets

I ask students to explain the transformations of the figures in this part.

  • Practice 1 - Describe the sequence of transformations that take place from Figure A to Figure B.
  • Practice 2 - A translation is a transformation that slides each point of a figure the same distance in the same direction. It basically slides the figure in on direction or another.
  • Practice 3 - These are bit more complex to attack.



Math Skill Quizzes

Each quiz focuses on a different questioning technique. See how it works for you.

  • Quiz 1 - Note the point of origin through out these shapes and placements.
  • Quiz 2 - Make sure you identify the shapes and their properties to help you through these.
  • Quiz 3 - If we transform the Figure B at the point (-2,-6) at 90˚ right then what will be the points?