Download Congruent shapes Congruent shapes have the same size and the

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
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
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
Congruent triangles
Congruent triangles have the same size and the same shape. When triangles are
congruent, all corresponding sides and corresponding angles are also congruent or
equal
For examples, the two triangles below are congruent
Corresponding angles are angles in the same position
Corresponding sides are sides that are in the same position
The two triangles above have a side with 3 markings. These sides are at the same
position and thus are corresponding
Congruent sides are sides that have equal measures
Congruent angles are angles that have equal sides and equal measures
In the triangle above, if we pull out the side with one and three markings and the
included angle, we get the following:
The above 45 degrees angle is a good example of congruent angles because the sides
are equal and the angles are equal
Included side: A side between two angles
Included angle: An angle between two sides
There are three postulates and two theorems that are used to identify if two triangles
are congruent
With these postulates and theorems, you don't have to check if all corresponding angles
and all sides are congruent
If the triangles meet the condition of the postulate or theorem, then, you have congruent
triangles.
They are the SSS postulate, SAS postulate, ASA postulate, AAS theorem, and
Hypotenuse-Leg theorem
SSS postulate:
If three sides of a triangle are congruent to three sides of a second triangle, then the two
triangles are congruent
Example:
ASA postulate:
If two angles and the side between these two angles (included side) of one triangle are
congruent to the corresponding angles and the included side of a second triangle, then
the two triangles are congruent
Example:
SAS postulate:
If two sides and the angle between these two sides (included angle) of one triangle are
congruent to the corresponding two sides and the included angle of a second triangle,
then the two triangles are congruent
Example:
AAS theorem:
If two angles and a side not between these two angles of one triangle are congruent to
two angles and the corresponding side not between these two angles of a second
triangle, then the two triangles are congruent
Example:
Hypotenuse-Leg theorem:
If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and
corresponding leg of a second right triangle, then the two triangles are congruent
Example: