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Section 4.5: Using Congruent Triangles. Goals. Use congruent ’s to prove other parts are congruent. Use congruent ’s to prove other geometric properties. Anchors. Identify and/or use properties of congruent and similar polygons Identify and/or use properties of triangles. Statements.

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Section 4.5:Using Congruent Triangles

Goals

  • Use congruent ’s to prove other parts are congruent.

  • Use congruent ’s to prove other geometric properties.

Anchors

  • Identify and/or use properties of congruent and similar polygons

  • Identify and/or use properties of triangles


Given w is the midpoint of qs pq ts and pw tw prove pwq tws

Statements

Reasons

Given: W is the midpoint of QS PQ  TS and PW  TWProve: PWQ  TWS

  • W is the mdpt of QS,

  • PQ  TS and PW  TW

  • Given

2) QW  SW

2) Def. of midpoint

3) PQW  TSW

3) SSS

4) PWQ  TWS

  • Corresponding Parts of Congruent Triangles are Congruent

CPCTC


Given qrs is isosceles rt bisects qrs qrs is the vertex angle prove qt st

Statements

Reasons

Given: QRS is isosceles RT bisects QRS QRS is the vertex angle Prove: QT  ST

)

  • QRS is isosceles

  • RT bisects QRS

  • Given

2) QRT  SRT

2)  bisector

3) QR  RS

3) Property of Isosceles 

4) RT  RT

4) Reflexive

5) QRT  SRT

5) SAS

6) QT  ST

6) CPCTC


Given b n rw bisects bn prove o is the midpoint of rw

)

)

Statements

Reasons

Given: B  N RW bisects BNProve: O is the midpoint of RW

)

)

  • B  N

  • RW bisects BN

  • Given

2) BOR  WON

2) Vertical Angles

3) BO  ON

3) Segment bisector

4) BRO  NWO

4) ASA

5) RO  OW

5) CPCTC

6) Definition of collinear

6) R, O, & W are collinear

7) Property of mdpt

7) O is the mdpt of RW


Given bn and rw bisect each other prove br wn

Statements

Reasons

Given: BN and RW bisect each otherProve: BR ║ WN

(

)

)

(

  • BN and RW bisect each other

  • Given

2) BOR  WON

2) Vertical Angles

3) BO  ON , RO  OW

3) Segment bisectors

4) BRO  NWO

4) SAS

5) B  N

5) CPCTC

6) If alt int s are  then the lines are ║

6) BR ║ WN


Given 1 2 fc bisects dcb prove afb efd

2

4

3

1

Statements

Reasons

Given: 1  2 , FC bisects DCBProve: AFB  EFD

)

)

)

)

)

  • 1  2 ,

  • FC bisects DCB

  • Given

2) 3  4

2) Angle Bisector

3) FC  FC

3) Reflexive

4) AFC  EFC

4) AAS

5) AF  EF

5) CPCTC

6) Vertical Angles

6) DFE  AFB

7) ASA

7) AFB  EFD


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