Transcript Link to Triangle Congruence Powerpoint

Congruent Triangles have six sets
of corresponding parts!
Three sets of corresponding sides
Three sets of corresponding angles
You don’t need to know all six sets of
corresponding parts to
determine congruence.
So, what information about two
triangles is enough to prove
congruence?
First: Some Terminology!
• Included Angle – The angle located BETWEEN
two adjacent sides
Angle B is the included angle
of sides AB and BC
• Included Side – The side located BETWEEN
two angles
Side MN is the included side between Angle M and Angle N
Can you make two triangles that are
NOT congruent using just
the given information?
If you can make two non-congruent triangles,
you don’t have enough information to prove
congruence
If you can’t make two non-congruent triangles,
then the information MUST BE ENOUGH TO
PROVE CONGRUENCE!
• Triangle ABC and DEF both have side lengths
of 5cm, 8cm and 11cm.
SSS Triangle Postulate
• Side – Side – Side (SSS)
IS ENOUGH TO PROVE CONGRUENCE.
These three measurements “LOCK IN” the the
angle measurements so all corresponding
parts are congruent.
Triangle ABC and Triangle DEF both have angles
that measure 40o, 60o and 80o
• Angle – Angle – Angle (AAA)
IS NOT ENOUGH TO PROVE CONGRUENCE.
• It is enough to prove similarity of triangles
• A dilation keeps the angles congruent but the
side lengths would change by the scale factor.
• Triangle ABC and DEF both have two sides
measuring 5cm and 11 cm with an included
angle of 60o.
SAS Triangle Postulate
• Side – Angle – Side (SAS)
IS ENOUGH TO PROVE CONGRUENCE.
These three measurements “LOCK IN” the other
three measurements so all corresponding
parts are congruent.
• Triangle ABC and Triangle DEF both have
angles that measure 40o and 60o and an
included side of 11 cm.
ASA Triangle Postulate
• Angle – Side – Angle (ASA)
IS ENOUGH TO PROVE CONGRUENCE.
These three measurements “LOCK IN” the other
three measurements so all corresponding
parts are congruent.
• Triangles ABC and DEF both have two angles
that are 60o and 80o and a non-included side
of 8 cm.
AAS Triangle Postulate
• Angle – Angle – Side (AAS)
IS ENOUGH TO PROVE CONGRUENCE.
These three measurements “LOCK IN” the other
three measurements so all corresponding
parts are congruent.
• Triangles ABC and DEF both have two sides
that are 8cm and 11cm and a non-included
angle of 40o.
There is a “Swing Effect” for
that 2nd side!
40o
TWO non-congruent triangles
can both have these two sides and
the non-included angle.
40o
• Side – Side – Angle (SSA)
IS NOT ENOUGH TO PROVE CONGRUENCE.
These three measurements do not lock in the
other three measurements because of that
“swing effect.”
Therefore, we cannot say two triangles are
congruent based on SSA.
• Right Triangle ABC and Right Triangle DEF both
have a leg 6cm and a hypotenuse 12cm.
12 cm
6cm
H-L TRIANGLE POSTULATE
• Hypotenuse-Leg (H-L)
IS ENOUGH TO PROVE CONGRUENCE for
RIGHT TRIANGLES.
The Pythagorean Theorem “LOCKS IN” the third
side because a2+b2=c2 is true for all right
triangles. HL is actually a special case of the
SSS Postulate.
SUMMARY
TRIANGLE CONGRUENCE
POSTULATES
Not Enough Information to Prove
Triangle Congruence
SSS : Side-Side-Side
AAA – proves similarity – the angles
make the triangle shape but do not
determine the size of the triangle
SAS: Side-Angle-Side
SSA – could be two different triangles
due to a “swing effect”
ASA: Angle-Side-Angle
AAS: Angle-Angle-Side
HL: Hypotenuse-Leg
(special case of SSS)
Are the two triangles congruent?
If so, which postulate is shown?