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Warm Up
Are the following triangles congruent? If so, by which theorem?
1)
2)
3)
4)
CPCTC
Essential Question:
What is CPCTC and how do you use it to prove
triangles are congruent?
Assessment:
Students will demonstrate in writing through
two column proofs in their notebooks
Key Concept
We know that in congruent figures corresponding
sides and angles are congruent.
This means that once you have shown that two
triangles are congruent using SSS, SAS, ASA, AAS, or
HL you know that all corresponding sides and all
corresponding angles are congruent.
– Corresponding Parts of Congruent Triangles are
Congruent
• Abbreviated CPCTC
Essential Question:
What is CPCTC and how do you use it to prove triangles are congruent?
Assessment:
Students will demonstrate in writing through two column proofs in their notebooks
Example
Tell what theorem shows that the triangles are
congruent and list all congruent sides and all
congruent angles.
Essential Question:
What is CPCTC and how do you use it to prove triangles are congruent?
Assessment:
Students will demonstrate in writing through two column proofs in their notebooks
Example
Tell what theorem shows that the triangles are
congruent and list all congruent sides and all
congruent angles.
Essential Question:
What is CPCTC and how do you use it to prove triangles are congruent?
Assessment:
Students will demonstrate in writing through two column proofs in their notebooks
Key Concept
CPCTC is used in proofs after
showing that triangles are congruent
as a reason for additional sides or
angles to be congruent.
Essential Question:
What is CPCTC and how do you use it to prove triangles are congruent?
Assessment:
Students will demonstrate in writing through two column proofs in their notebooks
Example: Prove the base angles theorem (If two sides of a
triangle are congruent then the angles opposite those sides are
also congruent.)
Given: In ΔABC (AB) ≅(AC) and (BD) is a perpendicular bisector
of (BC)
Show: ∠B ≅ ∠C
Statement
Reason
1. AB ≅ AC
1. Given
2. AD ⏊ bisector of BC 2. Given
3. AD ≅ AD
3. Reflexive Property
4. BD ≅ DC
4. Definition of perpendicular bisector
5. ΔABD ≅ ΔACD
5. SSS
6. ∠B ≅ ∠C
6. CPCTC
Pierre wishes to prove that ∠R ≅ ∠T in the isosceles triangle
shown below. Pierre knows that RS ≅ ST and he drew SU as
an angle bisector of ∠RST.
Part A:
Which triangle congruence postulate would prove that
ΔRUS ≅ ΔTUS?
Part B:
What is the last reason in the proof that proves ∠R ≅ ∠T?
Given: ABCD is a parallelogram
Prove: (AB) ≅(CD) and (BC) ≅(AD)
STATEMENTS
REASONS
1 ABCD is a
parallelogram
1
Given
2 Draw segment
from A to C
2
Two points determine one line
3 𝐴𝐵 ∥ 𝐶𝐷 and 𝐵𝐶 ∥ 𝐴𝐷
3
Definition of Parallelogram
4 ∠1 ≅ ∠2
∠3 ≅ ∠4
4
Alternate Interior Angles
5 𝐴𝐶 ≅ 𝐴𝐶
5
Reflexive Property
6 ΔABC ≅ ΔCDA
6
7 𝐴𝐵 ≅ 𝐶𝐷, 𝐵𝐶 ≅ 𝐴𝐷
7
ASA
CPCTC
Essential Question:
What is CPCTC and how
do you use it to prove
triangles are congruent?