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# 8.4 notes

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### 8.4 notes

1. 1. Tell how you know that the quadrilateral is a parallelogram. 1.The diagonals bisect each other. 2. Both pairs of opp <s ≅ ∴ opp sides //. Def of //ogram 3. For what value of x is the quadrilateral a parallelogram? 50 Bellwork 80 100 80 2x x + 30
2. 2. 8.4 Special Quadrilaterals Rhombus: w/ 4 ≅ sides Rectangle: w/ 4 right <s Square: w/ 4 sides ≅ & 4 right <s Rhombus Corollary: A quad is a rhombus iff it has 4 ≅ sides. Re ctangle Corollary: A quad is a rectangle iff it has 4 right <s. Sq uare Corollary: A quad is a square iff it is a rhombus and rectangle. Parallelograms Rhombuses Squares Rectangles
3. 5. A is a rhombus iff its diagonals are . A is a rhombus iff each diagonal bisects a pair of opposite <s. A is a rectangle iff its diagonals are ≅ . Theorem 8.11 Theorem 8.12 Theorem 8.13
4. 6. Theorem 8.11 Rewrite the theorem as a biconditional and prove it. Conditional Statement Converse PROOF: Statements Reasons ABCD is a //ogram Given Given <CXB & <DXC are right <s <CXB ≅ <DXC Def of right <s Questions to ask. What do I know about //ograms? What do I know about rhombuses? Reflexive Prop. SAS 6. CPCTC Transitive Prop. Def of rhombus ABCD is a rhombus A is a rhombus iff its diagonals are . If the diagonals of a are , then it is a rhombus. If the is a rhombus, then its diagonals are . Given: ABCD is a ; AC BD P rove: ABCD is a rhombus. A C D B X AC BD Def of lines DX ≅ BX Diagonals bisect each other in CX ≅ XC BXC ≅ DXC 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 1. 2. 3. 4. 5. 7. 8. 9. 10. 11. BC ≅ DC AD ≅ BC & DC ≅ AB Opp. sides of are ≅ AD ≅ DC & BC ≅ AB
5. 8. 8.4 HW pg . 537 #3 -51 multiples of 3