Properties of Quadrilaterals

 Opposite sides are parallel ( DC ll AB, AD ll BC )  Opposite sides are congruent ( DA CB, DC AB )  Opposite angles are congruent (<DAB <DCB, <ABC <ADC)  Diagonals bisect each other (DB bis. AC, AC bis. DB)  Consecutive angles are supplementary(<DAB suppl. <ADC, etc.)  Diagonals form 2 congruent triangles ( ABC CDA, DCB BAD)

 All properties of a parallelogram apply  All angles are right angles and.  Diagonals are ( ) AB CD

 Two disjoint pairs of consecutive sides are  Diagonals are  One diagonal is the bisector of the other  One of the diagonals bisect a pair of opposite <‘s  One pair of opposite <‘s are A B C D

 Parallelogram Properties  Kite Properties  All sides are congruent  Diagonals bisect the angles  Diagonals are perpendicular bisectors of each other  Diagonals divide the rhombus into 4 congruent rt. Triangles

 Rectangle Properties  Rhombus Properties  Diagonals form 4 isos. right triangles

 Exactly one pair of sides parallel

 Legs are congruent  Bases are parallel  Lower base angles are congruent  Upper base angles are congruent  Diagonals are congruent  Lower base angles are suppl. to upper base angles

Always, sometimes, never The diagonals of a rectangle are congruent Every square is a rectangle Every quadrilateral is a trapezoid In a trap. opp angles are congruent A rhombus is a rectangle An isos. trap is parallelogram Consecutive angles of a square are congruent Rhombuses are parallelograms Squares have only one right angle No trapezoid is a rectangle An isosceles trapezoid has no parallel lines Always Always Sometimes Never Sometimes Never Always Always Never Always Never

StatementsReasons Given: Triangle ACE is isos. With base AE CD CB AG FE BD GF Prove: BGFD is a parallelogram A B C D E FG 1.tri. ACE is isos. w/ base AE 2.CD CB 3.AG FE 4.BD GF 1. Given 2. Given 3. Given 4. Given 5. <A <E 5. If isos, then <‘s 6. CA CE 6. If <‘s, then sides 7. BA DE 7. Subtraction 8. Tri. BAG Tri. DEF 8. SAS(3,5,7) 9. BG DF 9. CPCTC 10. BGDF is a parallelogram 10. If opp. sides are then figure is a parallelogram

E Given: ABCD is a rhombus Prove: AC is perp. DB

StatementReason 1. ABCD is a rhombus 2. AD DC 3. DE DE 4. AE CE 5. Tri. ADE and Tri. CDE 6. <AED <CED 7. <AED and <CED are rt <s 8. AC DB E 1. Given 2. In a rhombus opp. Sides are 3. Reflexive 4. In a parallelogram diag. bisect each other 5. SSS(2,3,4) 6. CPCTC 7. If 2 <s are and suppl. They are rt. <s. 8. Rt <s are formed by perp. lines

CharacteristicsparallelogramrhombusrectanglesquaretrapezoidIsosceles trapezoid kite Both pairs of opp sides ll 1/2 Diag. Both pairs of opp sides are 1/2 At least 1 rt < Both pairs of opp. <s Cons. <s suppl 1/2 Diag form 2 tri. 1/2 Exactly 1 pair of opp. sides ll Diag. perp. Consecutive sides 1/2 Consecutive <s Diagonals bisect e.o. 1/2 Diagonals bisect opp. <s 1/2 All sides All <‘s

"Quickie Math." Quickie Math, n.d. Web. 19 Jan “Rhombus problems." analyze math. A Dendane, 5 November Web. 19 Jan Works Cited Rhoad, Richard, George Miluaskas, and Robert Whipple. Geometry for Enjoyment and Challenge. New Edition ed. Boston: McDougal Littell, Print.