Congruency and Symmetry
In these lessons, we will learn congruence of 2-D shapes and the symmetry of 2-D shapes. This lesson is suitable for Grade 3 and Grade 4 kids.
Congruence of 2-D Shapes
Two 2-D shapes are congruent if they are identical in shape and size.
It is important to recognize that the term congruent applies
only to size and shape. The figures can be different colors, or oriented in
different ways, and they will still be congruent as long as they are the same
shape and the same size.
Congruent shapes must have
• corresponding sides congruent
• corresponding vertices congruent
• the same area
• the same shape
The following Frayer Model gives a summary of congruency for 2-D shapes.
Congruent - Grade 4 Common Core Standards
This video examine the meaning of congruence.
Congruent Shapes and Angles.
Symmetry of 2-D Shapes
A 2-D figure has line symmetry when it can be
divided or folded so that the two parts match exactly.
The fold line is called the line of symmetry. Any given line of symmetry divides a
figure into equal halves. It may
also be said that each of the halves are mirror images of each other.
Line symmetry is also called reflective symmetry or
Symmetrical shapes must have:
• two congruent parts separated by a line of symmetry
• corresponding vertices and sides matching when the shape is folded along the axis of symmetry
The following Frayer Model gives a summary of symmetry for 2-D shapes.
Shapes may have multiple lines of symmetry and the lines of
symmetry can be vertical, horizontal, or diagonal. The more sides that a regular polygon has, the greater the number of
lines of symmetry there are. A circle has an infinite number of lines of symmetry.
Lines of symmetry - Grade 3 Common Core Standards
In this Video, we find lines of symmetry in a 2D shape.
Multiple Lines of Symmetry
Looking at a few problems with more than one line of reflective symmetry.
This video will review with you the basics of line symmetry and how to find line symmetry.
You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.