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# Goals - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' Goals' - garran

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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

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

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

)

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

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

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