Name: ate: Pd: Review Quadrilaterals PARALLELOGRAM Properties of a parallelogram: If a quadrilateral is a parallelogram, then 1. both pairs of opposite sides are parallel 2. both pairs of opposite sides are congruent 3. its diagonals bisect each other 4. both pairs of opposite angles are congruent 5. its consecutive angles are supplementary angles Sketch an example of a parallelogram. Ways to prove a quadrilateral is a parallelogram: A quadrilateral is a parallelogram if 1. both pairs of opposite sides are parallel 2. both pairs of opposite sides are congruent 3. its diagonals bisect each other 4. both pairs of opposite angles are congruent 5. one angle is supplementary to both consecutive angles 6. one pair of opposites sides both parallel and congruent RETANGLE Properties of a rectangle: If a parallelogram is a rectangle, it has all the properties of a parallelogram and 1. four right angles 2. congruent diagonals Sketch an example of a rectangle. Ways to prove a parallelogram is a rectangle: A parallelogram is a rectangle if 1. it has four right angles 2. it has congruent diagonals RHOMBUS Properties of a rhombus: If a parallelogram is a rhombus, it has all the properties of a parallelogram and 1. it has four congruent sides 2. its diagonals are perpendicular and bisect the opposite angles of the rhombus Sketch an example of a rhombus.
Ways to prove a parallelogram is a rhombus: A parallelogram is a rhombus if 1. it has four congruent sides 2. its diagonals are perpendicular SQUARE Properties of a square: If a parallelogram is a square, it has all the properties of a parallelogram and 1. it has four right angles and four congruent sides 2. its diagonals are congruent and perpendicular Sketch an example of a square. Ways to prove a parallelogram is a square: A parallelogram is a square if 1. it has four right angles and four congruent sides 2. its diagonals are congruent and perpendicular TRAPEZOI Properties of a trapezoid: If a quadrilateral is a trapezoid, it has at least one pair of parallel sides. A trapezoid is isosceles if it has one pair of congruent sides. Sketch an example of a trapezoid and an isosceles trapezoid: Trapezoid Isosceles trapezoid KITE Properties of a kite: If a quadrilateral is a kite, it has 2 pairs of congruent consecutive sides. Sketch an example of a kite:
Lesson 6.2 1. No; consecutive are not supplementary. 2. No; opposite are not. 3. yes 4. 3 5. 5 6. 4 7. 8 8. 5 9. 12 10. 37 11. 90 12. 53 13. 53 14. 20 15. 16. MP 8 2, NO 8 2 MP NO MN 4, PO 4 MN PO 17. slope MP slope NO 1 18. yes; parallel lines have equal slope. 19. yes; MQ 4 2, QO 4 2, MQ QO NQ 2 13, QP 2 13, NQ QP 20. 1. MATH 1. Given 2. MN AT 2. Given 3. AT MH, 3. Opposite sides of 4. MN MH 4. Transitive Property of 5. 1 2 5. opposite sides 21. 1. ATRO 1. Given 2. PT IP 2. Given 3. I T 3. opposite sides 4. T AOR 4. Opposite of a 5. I AOR 5. Transitive Property of
Lesson 6.3 1. yes 2. yes 3. no 4. no 5. no 6. yes 7. yes 8. yes 9. slope of AB slope 1and slope B slope A 5, so AB is by definition 10. AB 17 and B A 45 so AB is a since both pair of opposite sides 11. 8, 6, 0, 8, 8, 10 12. 6, 1, 0, 7, 4, 5 13. 1. Regular hexagon 1. Given JKLMNO 2. JO NM, 2. efinition of regular JK ML, polygon J M 3. OJK NML 3. SAS ongruence Postulate 4. OK NL 4. orresp. parts of s 5. ON KL 5. efinition of regular polygon 6. OKLN is a 6. If both pairs of opp. sides are, then quad. is a. 14. 1. VWKJ and SJRU 1. Given 2. W J, 2. Opp. of a J U 3. W U 3. Transitive Prop. of 15. Since AB is a, opposite sides So A B and segments contained within segments are also so AE BF. We know opposite sides of are so A B. Since E and F are given as midpoints we can show AE E and F FB, so through Segment Addition Postulate and ivision Property of Equality we can show AE FB. So quad. ABFE is a since one pair of opposite sides is and.
Lesson 6.4 1. 27 2. 54 3. 126 4. 54 5. 126 6. 90 7. 90 8. 63 9. true; false 10. false; true 11. true; false 12. false; false 13. true; true; a rhombus is a square if and only if it is a rectangle. 14. 11 15. 60 16. 10 17. 1. WHAT is a. 1. Given 2. W A 2. iagonals of bisect each other. 3. H T 3. iagonals of bisect each other. 4. ART is a 4. Given rhombus. 5. T A 5. efinition of rhombus 6. W H 6. Substitution A T 7. WA W A 7. Seg. Add. Postulate HT H T 8. WA HT 8. Substitution 9. WHAT is a 9. If diagonals of are rectangle, then it is a rectangle. 18. 1. GE GHX 1. Given 2. GE GH 2. orresp. parts of s 3. GEBH is a 3. Given 4. GH EB 4. If quad. is a, then opp. sides 5. GE HB 5. If quad. is a, then opp. sides 6. GE EB 6. Substitution 7. EB HB 7. Substitution 8. GEBH is a 8. A with 4 sides rhombus. is a rhombus. 19. 1. JXPE is a. 1. Given 2. EJ PX, EP JX 2. Opp. sides of 3. EX EX 3. Reflex. Prop. of 4. JXE PEX 4. SSS ongr. Postulate 5. J XPE 5. orresp. parts of s 6. XP EN 6. Given 7. XPE is a rt.. 7. efinition of 8. J is a rt.. 8. Substitution 9. JANE is a. 9. Given 10. J and A are 10. Adj. of supplementary. are supplementary. 11. A is a rt.. 11. If 2 are suppl. and one is a rt., then the other is a rt.. 12. N and PEJ 12. Opp. of a are rt.. 13. JANE is a 13. A with 4 rt. rectangle. is a rectangle.
Lesson 6.5 1. yes, no 2. no 3. yes, yes 4. 107 5. 129 6. 68 7. 20.5 8. 20 9. 7 10. WE SE 7.62; WT ST 10.44 11. m E m T 118 12. m T 113, m W 97 13. 60, 60, 120, 120 14. The sum of the lengths of the two bases is 12. 15. Statements Reasons 1. LORI is a rectangle. 1. Given 2. ILB and ROB 2. ef. of rectangle are rt.. 3. ILB RO 3. All right 4. LI OR 4. Opp. sides of 5. LB O 5. Given 6. LBI OR 6. SAS ongruence Postulate 7. BI R 7. orresp. parts of s 8. B IR 8. ef. of 9. BIR is an isos. trap. 9. ef. of isos. trap. 16. Statements Reasons 1. AF B 1. Given 2. AB A 2. Given 3. AB A 3. orresp. parts of s 4. F AB 4. Alternate Interior Thm. onverse 5. ABF is a trapezoid. 5. ef. of trapezoid
Lesson 6.6 1. A B 2. A rectangle B kite 3. A B 4. B isosceles trapezoid A rhombus 5. A B 6. sometimes 7. always 8. always 9. never 10. sometimes 11. never 12. sometimes square 13 15. Answers vary; Sample answers: 13. A B; with diagonals is a rectangle. 14. AB A; quad. with two pairs of consec. sides, but opposite sides is a kite. 15. A B; trap. with nonparallel sides is isosceles. 16. parallelogram; slope PQ slope RS 1 5 ; slope QR slope PS 1; adjacent sides 18 26 17. rectangle; slope PQ slope RS 1 4 ; slope QR slope PS 4; adjacent sides and not 17 68 18. trapezoid; slope PQ slope RS undefined; slope SP slope RQ 1 2 19. 5, 5.5, 8, 2, 7, 2.5, 4, 1 ; parallelogram