Congruent shapes

Congruent shapes have the same size and the same shape.In other words, if you place an object in front of a mirror, the image that you see is congruent or " equal " to the object

When shapes are congruent, all corresponding sides and angles are also congruent.

Look at the following two triangles.You should notice that some sides and some angles have one marking. Others have more than one

Congruent triangles

The side that has one marking corresponds to the other side that also has one marking.

and so forth...

The angle that has one marking corresponds to the other angle that also has one marking.

And so forth...

Having said that the best way to know if two figures are congruent is to compare the corresponding sides and corresponding angles

If these are equal, the figures are congruent. Therefore, be careful when doing your geometry problems about congruence.

Two figures may appear to be congruent yet one side or one angle in one shape may be slightly different than the other shape. Markings on shapes are the best way to compare sides and angles to see if they are equal or congruent

Circles too can be congruent. All circles have congruent angles since a complete turn measures 360 degrees for all circles

Therefore, it is up to the size of the circle and they will have the same size if they have the same radius

Congruent circles
Other examples of congruent shapes or figures

For the quadrilaterals, I used different markings for each side and each angles. Again, corresponding sides and angles have the same amount of markings

For the rectangles, I did not use four different markings although we have four sides. Since opposite sides are equal, I used the same marking for equal sides

The hexagon is a different story. I used the same marking for all angles and sides to keep the figure easy to read. However, at this point, you should be able to recognize corresponding sides and angles without major problems

See also:

congruent triangles
How to use postulates and theorems to check when two triangles are congruent

Similar shapes
Learn to identify when shapes are similar

Similar triangles
Use the angle angle similarity postulate to identify similar triangles

Page copy protected against web site content infringement by Copyscape

New Math Lessons

  1. Adding and Subtracting Integers game

    Oct 12, 15 11:12 AM

    Adding and subtracting integers game

    Read More

  2. Compensation in Math

    Sep 25, 15 11:35 AM

    Learn what compensation is in math. See how to use compensation to do mental math

    Read More

Bookmark and Share