1. Geometry Proofs
Unit 12
AA1.CC

2. Review: algebraic proof
Statement
Reason
5(x – 1) = 20 1. 2. 3.
4. x = 5 4.

3. Example1: Proving CongruenceB D E C
Given: CE = ED, AE = EB
Prove:
STATEMENTS
REASONS
1. CE = ED
Given 2.
2. Definition of ≅ segments
3. AE = EB 3.
4. 𝐴𝐸 ≅ 𝐸𝐵 4. 5.
5. Vertical Angles Theorem

4. Example 2: Proving Congruence
Given:
Prove: A B D C
STATEMENTS
REASONS 1.
1. Given 2.
2. Given 3.
3. Reflexive property 4.

5. Example 3: Proving Congruence
Given: 𝐴𝐷 ≅ 𝐶𝐷 , 𝐴𝐵 ≅ 𝐶𝐵
Prove: B A C D
STATEMENTS
REASONS 1.
1. Given
2. 𝐴𝐵 ≅ 𝐶𝐵 2. 3. 4.

6. If ∆𝐴𝐵𝐶≅∆𝐷𝐸𝐹, then what do you know about their sides and angles???
Their corresponding sides are congruent!!!
Their corresponding angles are congruent!!!
Sides:
𝐴𝐵 ≅ 𝐷𝐸
𝐵𝐶 ≅ 𝐸𝐹
𝐴𝐶 ≅ 𝐷𝐹
Angles:
∠A ≅ ∠D
∠B ≅ ∠E
∠C ≅ ∠F
*This is ‘CPCTC’ – a reason we can use in a poof!!!!

7. 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.

8. Example: Prove: AB ≅ DE 1. AC ≅ DF 2. ∠C ≅ ∠F 3. CB ≅ FE
Statements Reasons B C
1. AC ≅ DF
2. ∠C ≅ ∠F
3. CB ≅ FE
4. ΔABC ≅ ΔDEF
5. AB ≅ DE D F E

9. Example A B E C D Given: As marked in diagram Prove: CE  DE
Statements
A  B
AC  BD
AEC  BED
ΔAEC  ΔBED
CE  DE
Reasons 1. 2. 3. 4. 5.