1. NOTES 3.3
CPCTC

2. Congruent triangles: triangles whose corresponding parts are congruent.
CPCTC
Corresponding Part of Congruent Triangles are Congruent.
This can be used in a proof only AFTER triangles have been proven congruent.

3. N M O L Example 2: Given: ⨀O 𝑁𝑂 ⊥ 𝐿𝑀 Prove: ∆NOL  ∆NOM
𝑁𝑂 ⊥ 𝐿𝑀
Prove: ∆NOL  ∆NOM L M O N
Statements
Reasons
1. ⨀O
1. Given 2. 3. 4. 5. 6. 7.
All radii of a circle are congruent
Given
NOL and NOM are right angles
If lines perp, then right angles
NOL  NOM
All right angles are congruent
ON  ON
Reflexive Property
∆NOL  ∆NOM
SAS

4. If comp to same angle, then 
Example 3:
Given: Z is the midpoint of
Y and W are complementary to V
Prove: W Z V X Y
Statements
Reasons 1.
1. Given 2. 3. 4. 5. 6. 7. 8.
Z is the midpoint of
If mp, then  segments
Y and W are comp. to V
Given
Y  W
If comp to same angle, then 
VZY  WZX
Vertical angles are 
∆VZY  ∆XZW
ASA
CPCTC

5. All radii of a circle are congruent
Example 4:
Given: ⨀P
Prove: L M N P K
Statements
Reasons
1. ⨀𝑃
1. Given 2. 3. 4. 5.
All radii of a circle are congruent
KPL  NPM
Vertical Angles are 
∆VZY  ∆XZW
SAS
CPCTC

6. T Q R S Example 5: Given: ⨀Q RT = TS Prove: TRQ  TSQ
Statements
Reasons
1. ⨀Q
1. Given 2. 3. 4. 5. 6.
All radii of a circle are congruent
RT = RS
Given
Definition of congruent
∆TRQ  ∆TSQ
SSS
TRQ  TSQ
CPCTC

7. F A E B C D Example 6: Given: C is the midpoint of AC = CE
Prove: ∆ABF  ∆EDF A E B C D
Statements
Reasons 1.
1. Given 2. 3. 4. 5. 6. 7. 8.
FCA and FCE are right angles
If perp lines, then right angles
FCA  FCE
All right angles are congruent
Reflexive Property
If = then 
∆FCA  ∆FCE
SAS
A  E
CPCTC
Continued on next slide