Post on 13-Dec-2015
(4.4) CPCTC Corresponding Parts of Congruent Triangles Congruent
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.
Proving Triangles Congruent
Can we use (SSS, SAS, AAS, or ASA) the given information to prove triangles congruent?
ASA AAS Not Possible
SSS Seriously? SAS
Proving Triangles Congruent
Given Look For… Reason Example
Midpoint Two segments are congruent
Defn. of midpoint
Segment bisects a segment
Two segments are congruent
Defn. of bisector
D
B C
EA
If E is the midpoint of AC
then AE CE
If AC bisects BD
then BE DE
Two segments parallel
Alt. int. angles congruent
Alt. int. angles theorem
If BA ||CD
then AC
and BD
Vertical angles Two congruent angles
Vert. angles theorem
BEADEC
Proving Triangles Congruent
Segment bisects an angle
Two anglesare congruent
Defn. of angle bisector
Triangles that share a side
A segment congruent to itself
Reflexive property of congruence
Given Look For… Reason Example
X
YW Z
If XZ bisects WXY
then WXZ YXZ
XZ XZ
Perpendicular segments
Two anglesare congruent
1) Right angles by defn. of lines
2) All right angles
If XZWYthen 1, 2 are right 's
then 12
1 2
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.
Proving Triangles Congruent
X
YW ZYXZWXZ
WYXZ
WXYXZ
:Prove
bisects :Given
YXZWXZ
WYXZ
Proving Triangles Congruent
D
B C
E
A
CA :Prove
and ofmidpoint theis E :Given
BDAC
BDAC and ofmidpoint theis E
CEDAEB CEDAED
CA
homework
1. Sticker #3 Due: Wed. 1/29
2. Sticker #4 Due: Fri. 1/31
3. Practice WS (4.4) Due: Wed. 1/29
4. Study Island Challenge Due: Wed. 3/12
5. Update 3 x 5 Cards