Warm Up #3
April 20th
Proofs for Triangles
Monday April 20th
Proofs
• Follow a problem step-by-step with
justification or reasoning for each
step.
• 2-Column Proofs
• Flow Chart Proofs
General Format
• For proofs, we will be given 2 statements;
the GIVEN and PROVE
• Always start with the Given information
• We end the proof with the Prove
statement
• The reason for each step is an explanation
as to HOW you got the information from
previous steps
2-Column Proofs
• One Column is titled “Statements” and the other
“Reasons”
• Any statement must come from the given
information, the picture, or come from previous
steps
Just
An
example
Statement
Reason
1. YA≌AB
1. Given
2. <Y≌<B
2. Given
3. <YAZ≌<CAB
3. Vert. < Thm.
4. ∆ZAY≅ ∆CAB
4. ASA Postulate
5. ZA≅AC
5. CPCTC
Write a 2-Column Proof
• Given: 5 + 2(y + 4) = 5(y - 3) + 10
• Prove: y = 6
Statements
1.
2.
3.
4.
5.
6.
Reasons
1.
2.
3.
4.
5.
6.
Flow Chart Proofs
• You can start a column with any of the following
information
• Given
• Reflexive Statements
• Information from the picture
• Flow Chart proofs have lines connecting related
information
• The statements are in the bubbles, and the reasons
are written below.
Given: KJ ≅ MN, <J ≅ <N
Prove: ∆KJL ≅ ∆MNL
SSS (2-Column)
• Given: MO≌LK and KM≌OL
• Prove: ∆KOM ≌ ∆OKL
Statements
1. MO≌LK
≌ and KM≌OL
≌
2. KO≌KO
≌
3. ∆KOM ≌ ∆OKL
Reasons
Given
Reflexive
SSS Postulate
SSS Flowchart Proof
Given: MO≌LK and KM≌OL
Prove: ∆KOM ≌ ∆OKL
ASA (2-Column)
• Given: <Y≅<B and YA≅BA
• Prove: ∆ZAY≅ ∆CAB
Statements
1. <Y≅<B
≅ and YA≅BA
≅
2. <ZAY≅<CAB
3. ∆ZAY≅ ∆CAB
Reasons
Given
Vertical < Thm
ASA Postulate
ASA Flowchart
Given: <Y≅<B and YA≅BA
Prove: ∆ZAY≅ ∆CAB
Fill in the Missing Info!
• Given: DA≅MA, AJ≅AZ
• Prove:∆ JDA ≅ ∆ ZMA
CPCTC:
Corresponding Parts of Congruent
Triangles are Congruent
CPCTC
Definition of Congruent Triangles
• If two triangles corresponding parts are
congruent, then the triangles are congruent.
• This allows us to use the congruent triangle methods (SSS,
ASA, SAS, AAS, HL)
• If two triangles are congruent, then their
corresponding parts are congruent.
• This is where we use CPCTC. Use after we have found SSS,
ASA, SAS, AAS, HL
In a proof…
• Use congruent parts to determine SSS, ASA, SAS,
AAS, HL to show two triangles are congruent.
• Then use CPCTC to show corresponding parts of
the same triangles are congruent.
When do we use CPCTC?
• Given: YA≌AB, <Y≌<B
• Prove: ZA≌AC
Statement
Reason
1. YA≌AB
1. Given
2. <Y≌<B
2. Given
3. <YAZ≌<CAB
3. Vert. < Thm.
4. ∆ZAY≅ ∆CAB
4. ASA Postulate
5. ZA≅AC
5. CPCTC
Classwork
• Complete the proofs on the back of the last page of notes!
Homework
• Continue working on Weekly #6
•#’s 15-26
•PROOFS WORKSHEET