Download 4-4 Isoceles Triangles, Corollaries and CPCTC

Isosceles Triangles,
Corollaries, &
CPCTC
Corresponding parts of congruent
triangles are congruent.
Corresponding parts of congruent
triangles are congruent.
Corresponding parts of congruent
triangles are congruent.
Corresponding parts of congruent
triangles are congruent.
Corresponding Parts of Congruent
Triangles are Congruent.
CPCTC
If you can prove
congruence using a
shortcut, then you
KNOW that the
remaining
corresponding parts
are congruent.
You can only use
CPCTC in a proof
AFTER you have
proved
congruence.
Corresponding parts
When you use a shortcut (SSS, AAS, SAS, ASA,
HL) to show that 2 triangles are congruent,
that means that ALL the corresponding parts are
congruent.
EX: If a triangle is congruent by ASA (for
instance), then all the other corresponding parts
are congruent.
B
F
That means that EG  CB
A
E
C
What is AC congruent to?
G
FE
For example:
A
Prove: AB  DE
Statements
B
C
D
AC  DF
Given
<C  <F
Given
CB  FE
Given
ΔABC  ΔDEF
SAS
AB  DE
F
E
Reasons
CPCTC
Get:
a piece of patty paper
a straight edge
your pencil
your compass
We are going to create an
isosceles triangles with 2
congruent sides.
Isosceles Triangles
♥ Has at least 2 congruent sides.
♥ The angles opposite the congruent
sides are congruent
♥ Converse is also true. The sides
opposite the congruent angles are
also congruent.
♥ This is a COROLLARY.
A corollary naturally follows a
theorem or postulate. We can
prove it if we need to, but it really
makes a lot of sense.
♥ The bisector of the vertex angle of an
isosceles Δ is the perpendicular bisector of
the base.
Vertex angle
Base
In addition, you just learned
that the angles opposite
congruent sides are
congruent…
Your
assignment
4.4 Practice Worksheet
4.5 Practice Worksheet