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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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