SAS Criteria of Congruence
Sam and Roy started playing a game.
First Sam drew a triangle with measurements as shown.
Later, Sam asked if Roy could draw the same triangle without actually seeing what Sam drew.
For that Roy asked Sam to provide some information to draw the same triangle.
So, Sam asked Roy to draw a
$△LMN$
, where one side is of length 5.5cm.
Roy could draw many triangles that have a side of length 5.5cm.
So, Roy asked for some more information from Sam.
This time Sam told him that the triangle has one side of length 5.5cm and an angle of
$65_{o}$
Even with this information, Roy could draw many triangles as shown.
Then, Sam gave the lengths of two sides as
$5.5cm$
and
$3.4cm$
, and the angle between these two sides as
$65°$
So, Roy started constructing a triangle with this information.
First, Roy drew LM of length 5.5. cm.
Then, Roy constructed an angle of
$65_{o}$
at M as shown.
Roy took a measure of 3.4 cm using a compass and a scale as shown.
Using this measure on the compass, Roy marked an arc from M as shown.
Now Roy joined N to L using a scale as shown.
And
$△LMN$
constructed by Roy is congruent to
$△ABC$
Here the information used about the triangles is the measures of their side-angle-side.
So by using SAS criterion we can say that the two triangles are congruent without even comparing them.
If two sides of a triangle and the angle included between them are equal to two sides and the angle included between them of another triangle...
Then the two triangles are congruent by SAS Criterion.
Revision
If two sides and the angle included between them of a triangle are equal to two sides and the angle included between them of another triangle...
Then the two triangles are congruent by SAS Criterion
The End