Congruent Shapes

In mathematics, congruent shapes are shapes that have the same size and shape. This means that if you were to place one shape on top of the other, they would perfectly overlap. Congruent shapes are identical in every way, including their angles and side lengths.

When comparing two shapes to see if they are congruent, you can use a few different methods:

Side-Length Comparison: You can measure the sides of the shapes and compare their lengths. If all corresponding sides are equal, then the shapes are congruent.
Angle Comparison: You can compare the angles of the shapes. If all corresponding angles are equal, then the shapes are congruent.
Overlapping: You can physically place one shape on top of the other to see if they overlap perfectly. If they do, then the shapes are congruent.

It's important to note that congruent shapes can be in different orientations or positions. As long as the shapes have the same size and shape, they are considered congruent.

When working with congruent shapes, it's common to use the symbol ≅ to represent congruence. For example, if shape A is congruent to shape B, it would be written as A ≅ B.

Understanding congruent shapes is important in geometry and can be used to identify and classify different types of shapes and figures.

Overall, congruent shapes are identical in every way and provide a fundamental concept in the study of geometry.

◂Math Worksheets and Study Guides Third Grade. Congruent Shapes

Vocabulary/Answer key

Congruent Shapes

The resources above cover the following skills:

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes.

Classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids.

Explore congruence and similarity.

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life.

Grade 3 Curriculum Focal Points (NCTM)

Geometry: Describing and analyzing properties of two-dimensional shapes

Students describe, analyze, compare, and classify two-dimensional shapes by their sides and angles and connect these attributes to definitions of shapes. Students investigate, describe, and reason about decomposing, combining, and transforming polygons to make other polygons. Through building, drawing, and analyzing two-dimensional shapes, students understand attributes and properties of two-dimensional space and the use of those attributes and properties in solving problems, including applications involving congruence and symmetry.