Download Ways to prove Triangles Congruent

Ways to prove Triangles
Congruent
Method: Side-Side-Side (SSS)
Description: Three corresponding
sides are congruent from one
triangle to another.
(SSS is a Postulate)
Method: Side-Angle-Side (SAS)
Description: Two corresponding
sides and the included angle are
congruent to the corresponding
parts of another triangle.
Method: Angle-Side-Angle (ASA)
Description: Two angles and the
included side are congruent from
one triangle to another triangle.
Method: Angle-Angle-Side
(AAS)
Description: By using ASA, we
know the third angle in one
triangle must be congruent to
the third angle in the other
triangle since the angle sum
must be 180 degrees.
(AAS is a Theorem and is a
shortcut of the ASA Postulate)
Ways to Prove Right Triangles
Congruent
*Keep in mind each of these methods
only contain 2 letters because the right
angle of the triangle is always a given
so it is not included as one of the
letters.
Method: Leg-Leg (LL)
Description: Same as SAS but the
“A” is the right angle and so you
are left with just two sides or
“legs” of the right triangle.
Method: Leg-Angle (LA)
Description: Same as ASA or AAS but
one of the angles is the right angle so
you are left with just one angle and
side or an angle and a leg.
Like ASA
or
Like AAS
Method: Hypotenuse-Angle (HA)
Description: Same as AAS but one
of the angles is the right angle the
other angle is one of the acute
angles and the side is the
hypotenuse of the triangle.
Method: Hypotenuse-Leg (HL)
Description: This is really Angle-SideSide (can’t use…spells bad word), but
it only works when the angle is a right
angle, so you are left with the sides
being a leg and hypotenuse of the
right triangle.
Ways that you CANNOT prove
triangles congruent
Method: Angle-Side-Side (ASS)
Reason cannot be proven: If you
draw two triangles with one
congruent angle and one congruent
side next to the angle, the next side
can still be the same length on both
triangles, but it can move to change
the measure of the angle…therefore
the triangles would not be congruent.
*There is one exception…this is when
the angle is a right angle as
mentioned above.
Method: Angle-Angle-Angle
(AAA)
Reason cannot be proven: Just
because the three angles are
congruent in two triangles
does not necessarily mean that
they are congruent, because
they could be different sizes
which would make
them similar.