Download Side-Side-Side (SSS) - Old Saybrook Public Schools

February 7, 2017
Proving triangles congruent
It turns out that you can prove two triangles are
congruent with just 3 pairs of corresponding parts, if
the three measurements determine a unique triangle.
But, not all combinations of 3 parts will determine a
unique triangle.
Let's look at the different combinations. There are
6 in total.
Side-Side-Side (SSS)
February 7, 2017
Side-Angle-Side (SAS)
The angle is between the 2 sides.
(The 2 sides of the triangle form the angle.)
Draw your own triangle and mark two sides and the angle
between them.
Angle-Side-Angle (ASA)
The side is between the two angles. The side is
connected to both angles.
Draw your own triangle and mark it with ASA
February 7, 2017
Angle-Angle-Side (AAS)
The side only connects with the vertex of one angle.
(The side is not between the two angles. The side is
not connected to both angles)
Draw your own triangle and mark it with AAS
Side-Side-Angle (SSA)
The angle is not formed by the two sides of the
triangle. The angle is not between the two sides.
(The angle is not formed by the 2 sides.)
Draw your own triangle and mark it with SSA.
February 7, 2017
Angle-Angle-Angle (AAA)
Do the markings on the triangle represent
SSS, SAS, AAS, ASA, AAA, or SSA?
1.)
SAS
2.)
SSA
3.)
AAS
February 7, 2017
So which combinations prove that two triangles are
congruent?
Let's investigate.
Given 3 measurements, try to draw two different
triangles that have the 3 given measurements. If you
can draw two different triangles, then the
measurements do not determine a unique triangle and
do not prove that two triangles are congruent.
Now we will investigate the other combinations of
measurements.
http://illuminations.nctm.org/activity.aspx?id=3504
February 7, 2017
Triangle congruence theorems