Section 4.3 & 4.4: Proving s are Congruent

Section 4.3 & 4.4: Proving s are Congruent Goals • Identify  figures and corresponding parts • Prove that 2  are  Anchors • Identify and/or use properties of congruent and similar polygons • Identify and/or use properties of triangles

M Q N R P S Side-Side-Side (SSS)  Postulate • If If Then Then we can say:

Statements Reasons Given: W is the midpoint of QS PQ  TS and PW  TWProve: PQW  TSW

Statements Reasons Given: D is the midpoint of ACABC is isoscelesProve: ABD  CBD

Q X P W S Y Side-Angle-Side (SAS)  Postulate • If If ) ) Then Then we can say:

Statements Reasons Given: QRS is isosceles RT bisects QRSProve: QRT  SRT

Statements Reasons Given: BD and AE bisect each otherProve: ABC  EDC

) Q M ) R N S P ) ) Angle-Side-Angle (ASA)  Postulate • If If Then Then we can say:

Statements Reasons Given: B  N RW bisects BNProve: BRO  NWO

1 3 4 2 Statements Reasons Given: 1  2 CD bisects BCEProve: BCD  ECD

Q X ) ) P W S Y ) ) Angle-Angle-Side (AAS)  Theorem • If If Then Then we can say:

Statements Reasons Given: AD ║ EC , B is the mdpt of CDProve: ABD  EBC

40 40 50 50 Why Angle-Angle-Angle (AAA)Doesn’t Work

E ( A D F ( C B Why Side-Side-Angle (SSA)Doesn’t Work

Theorem 4.8: Hypotenuse-Leg (HL)  Theorem • If D A If Then B C E F Then we can say:

Statements Reasons Given: RS  QT QRT is isoscelesProve: QRS  TRS

Section 4.3 & 4.4: Proving s are Congruent