1. (4.4) CPCTC Corresponding Parts of Congruent Triangles Congruent

2. Proving Triangles Congruent
LT: To use triangle congruence and CPCTC to prove that parts of two triangles are congruent. Relevancy: This concept of CPCTC can be used measure distance indirectly.

3. Proving Triangles Congruent
Can we use (SSS, SAS, AAS, or ASA) the given information to prove triangles congruent?
Not Possible
ASA
AAS
SSS
Seriously? 
SAS 3

4. Proving Triangles CongruentD B C E A
Given
Look For…
Reason
Example
Two segments
are congruent
Midpoint
Defn. of midpoint
Segment bisects
a segment
Two segments
are congruent
Defn. of bisector
Two segments parallel
Alt. int. angles congruent
Alt. int. angles theorem
Vertical angles
Two congruent angles
Vert. angles
theorem

5. Proving Triangles CongruentX 1 2 W Z Y
Given
Look For…
Reason
Example
Segment bisects
an angle
Two angles
are congruent
Defn. of
angle bisector
Triangles that
share a side
A segment congruent to itself
Reflexive property of congruence
Perpendicular segments
Two angles
are congruent
1) Right angles by defn. of lines
2) All right angles

6. Proving Triangles Congruent
With SSS, SAS, ASA, and AAS; you know how to use three parts of triangles to show that the triangles are congruent. Once you have triangles congruent, you can make conclusions about their other parts because by definition, Corresponding Parts of Congruent Triangles are Congruent (CPCTC) **You can use CPCTC in a proof. 6

7. Proving Triangles CongruentX W Z Y
Statement
Reason
1. Given 2.
2. Given
3. Defn. of Angle Bisector
4. Right angles are congruent because of defn. of perpendicular lines
5. Reflexive Property of ≌ 6.
6. ASA

8. Proving Triangles CongruentB C E A D
Statement
Reason 1.
1. Given
2. Defn. of Midpoint 3.
3. Vertical Angles 4.
4. SAS 5.
5. CPCTC

9. homework Sticker #3 Due: Wed. 1/29 Sticker #4 Due: Fri. 1/31
Practice WS (4.4) Due: Wed. 1/29
Study Island Challenge Due: Wed. 3/12
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