Ch 4 Notesheet Key

Ch 4 Note Sheet L1 Key
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4.6 Corresponding Parts of Congruent Triangles
Note: Once you can prove that two triangles are congruent, by using the conjectures above, then any of
the corresponding parts will be equal.
Definition of Congruent Triangles:
If two triangles are congruent, then all of their corresponding parts (sides and angles) are
congruent.
Can also be stated “Corresponding Parts of Congruent Triangles are Congruent” or
CPCTC.
When you write congruent triangles you must match the corresponding vertices. (To show how the match up.)
So if you know that ΔCAT
≅ ΔDOG
then you can say any of the following:
∠C
≅ ∠ D CA ≅ DO
∠A
≅ ∠ O AT ≅ OG
∠T
≅ ∠ G CT ≅ DG
Examples: How to prove (show deductively) that parts are equal.
First example, informal paragraph :
P
Know: ∠PAC ≅ ∠TAC
and PA AT
Is ∠PCA ≅ ∠ TCA ?
≅ .
A
T
The triangles share a side, so CA
So…
= CA of course.
C
ΔPAC
≅ ΔTAC
by SAS Congruence
and ∠PCA ≅ ∠ TCA because CPCTC or Corresponding Parts of Congruent Triangles are
Congruent.
A bit more formal paragraph:
Given: Z is midpoint of DI and EP .
Z
Prove: PI ≅ DE ?
Z is midpoint of DI and EP was given, so
IZ = ZD and PZ = ZE by Definition of Midpoint
D
E
∠PZI
≅ ∠ EZD by the Vertical Angles Conjecture (or vertical angles are congruent.)
Therefore, ΔZIP ≅ ΔZDE
by SAS Congruence and
PI DE
≅ because CPCTC or Corresponding Parts of Congruent Triangles are Congruent.
P
I
S. Stirling Page 10 of 15