Goals

1. 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

2. 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

3. 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

4. ) ) 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

5. 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

6. 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