(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