Unit 5 Review. For each problem (1-4) a and b are segment lengths; x and y are angle measures.

Transcription

1 For ech problem (1-4) nd b re segment lengths; x nd y re ngle mesures. 1. Figure is Prllelogrm 2. Figure is Squre b b = 21 b = 16 x = 104 y = 40 = 3 2 b = 6 x = 45 y = Figure is Rectngle 4. Figure is Rhombus b = b = 3.2 b = 6 b = 3.2 x = 65 x = 90 y = 50 y = TR + TR = RN 2x + 2x = 5x 9 4x = 5x 9 -x = -9 x = 9 T R 8. x + 7 2y T = RN 4x + 9 = 9x = 5x x = 3/5 5. If TR = 2x nd RN = 5x - 9,then x = If T = 4x + 9 nd RN = 9x + 6, then x = 3/5. 7. If T = 16, then TN = 24. (Ech piece is 8). N 5x - 2 2y 7 = y + 18 y = 25 x x + 7 = 5x 2 2x + 14 = 5x 2 16 = 3x x = 16/3 y + 18 x = 16/3 y = 25

2 is rectngle = x 2 = x + 72 x 2 = x + 72 x 2 x 72 = 0 (x 9)(x + 8) = 0 x = 9, x = -8 is squre m = 4x + 4y m = 8x 4y 4x + 4y = 90 8x 4y = 90 12x = 180 4(15) + 4y = 90 x = is rhombus m = 15y - 35 m = 20x m = 80 15y 35 = y = 135 y = 9 x = 9 x = -8 4y = 30 y = 7.5 x = 15 y = x = 100 x = 5 x = 5 y = y is prllelogrm m = 5x + 9 m = 7x + 3 5x x + 3 = x + 12 = x = 168 x = 14 x = 14 y = 101 E F is trpezoid; EF is the medin E = 5x - 7 F = y 2 = 6x + 2 F = -y + 6 E + E = 5x 7 + 5x 7 = 6x x 14 = 6x + 2 4x = 16 x = 4 y 2 = -y + 6 y 2 + y 6 = 0 (y + 3)(y 2) = 0 x = 4 y + 3 = 0; y = -3 y = -3 y 2 = 0; y = 2 y = 2 E F is n isosceles trpezoid EF is the medin = 8x - 2 EF = 3x + 7 = 3x + 6 EF 2 8x 2 3x 6 3x x 4 6x 14 5x 10 x 2 x = 2

3 Property Prllelogrm Rectngle Rhombus Squre ll ngles re right ngles x x oth Pirs of Opposite sides re prllel x x x x ll sides re congruent x x oth Pirs of Opposite ngles re congruent x x x x igonls bisect interior ngles of qudrilterl x x igonls re perpendiculr x x igonls re congruent x x igonls bisect one nother x x x x oth Pirs of Opposite sides re congruent x x x x True nd Flse Flse 1. ll qudrilterls re prllelogrms. True 2. ll prllelogrms re qudrilterls. True 3. ll squres re rhombi. True 4. ll rectngles re prllelogrms. Flse 5. If prllelogrm hs ^ digonls nd four congruent sides it must be squre. Flse 6. If digonls of qudrilterl re congruent, then the qudrilterl is prllelogrm. Flse 7. n isosceles trpezoid hs two congruent bses. True 8. If digonls of qudrilterl bisect one nother, then the qudrilterl is prllelogrm. Flse 9. ll trpezoids re prllelogrms. Flse 10. ll prllelogrms re rectngles. True 11. If both pirs of opposite ngles of qudrilterl re congruent, then the qudrilterl is prllelogrm. True 12. ll trpezoids re qudrilterls. Flse 13. If one pir of opposite sides in qudrilterl re prllel, then the qudrilterl is prllelogrm. Flse 14. ll rhombi re squres. True 15. The sum of the interior ngles of trpezoid is 360. True 16. squre hs congruent digonls. Flse 17. trpezoid cn hve four congruent sides. Flse 18. The digonls of rhombus re lwys congruent. True 19. If one pir of opposite sides in qudrilterl re prllel nd congruent, then the qudrilterl is prllelogrm. Flse 20. ll rectngles hve perpendiculr digonls. True 21. igonls of rhombus bisect one nother. True 22. n isosceles trpezoid hs congruent legs. True 23. trpezoid cn hve no congruent sides. Flse 24. The legs of trpezoid re prllel. Flse 25. If two lines hve equl slopes, then the lines re perpendiculr.

4 omplete the blnk with the word lwys, sometimes or never. 1. squre is LWYS rhombus. 2. The digonls of prllelogrm LWYS bisect one nother. 3. prllelogrm with four congruent sides is SOMETIMES rectngle. 4. The digonls of rhombus re SOMETIMES congruent. 5. rectngle LWYS hs opposite sides tht re congruent. 6. prllelogrm SOMETIMES hs perpendiculr digonls. 7. rectngle is SOMETIMES squre. 8. squre is LWYS rectngle. 9. prllelogrm LWYS hs opposite congruent ngles. 10. rhombus is SOMETIMES rectngle. 11. rhombus LWYS hs perpendiculr digonls. 12. trpezoid is NEVER prllelogrm. 13. rectngle LWYS hs congruent digonls. 14. squre LWYS hs four congruent sides. 15. prllelogrm SOMETIMES congruent digonls. 16. prllelogrm is SOMETIMES squre. 17. rectngle SOMETIMES hs perpendiculr digonls. 18. rectngle is SOMETIMES rhombus. 19. trpezoid NEVER hs two pirs of opposite prllel sides. 20. squre is LWYS rhombus. 21. rhombus is SOMETIMES squre. 22. rhombus SOMETIMES hs four right ngles. 23. prllelogrm with congruent digonls nd four right ngles is LWYS rectngle. 24. Opposite sides of prllelogrm re LWYS congruent. 25. The legs of trpezoid re SOMETIMES congruent. 26. rhombus SOMETIMES hs four congruent ngles. 27. prllelogrm hs interior ngles tht LWYS dd up to squre is NEVER trpezoid. 29. The bses of trpezoid re LWYS prllel. 30. trpezoid is NEVER rhombus. 31. rhombus SOMETIMES hs congruent digonls. 32. squre is LWYS prllelogrm. 33. The legs of trpezoid re NEVER prllel. 34. The bses of trpezoid re NEVER congruent.

5 Given: GF is GH H Sttements G H F Resons 1. GF is prllelogrm 1. Given GF 2. Opposite sides of prllelogrm re congruent. 3. // GF; G // F 3. efinition of Prllelogrm If two prllel lines re cut by trnsversl, then lternte interior ngles re congruent If two prllel lines re cut by trnsversl, then corresponding ngles re congruent Substitution GH 7. Given FHG 8. SS H 9. PT Given: LQM Prove: KMLJ is prllelogrm K Q M J L Sttements Resons 1. LQM 1. Given 2. MLQ 2. PT 3. KJ // LM 3. If two lines re cut by trnsversl nd lternte interior ngles re congruent, then the lines re prllel. 4. LM 4. PT 5. KMLJ is prllelogrm 5. If one pir of opposite sides of qudrilterl re both prllel nd congruent, then the qudrilterl is prllelogrm.

6 H T X M 1. TH nd T: If both pirs of opposite sides re congruent, then the qudrilterl is prllelogrm. 2. M // TH nd TH: If one pir of opposite sides re both congruent nd prllel, then the qudrilterl is prllelogrm. 3. XM nd HX: If the digonls bisect one nother, then the qudrilterl is prllelogrm. 4. T nd HT // M: NO 5. MHT nd HT: If both pirs of opposite ngles re congruent, then the qudrilterl is prllelogrm. 6. TX nd HT: NO 7. X is the midpoint of MT nd H: If the digonls bisect one nother, then the qudrilterl is prllelogrm. 8. HT nd MH: ecuse the pirs of lternte interior ngles re congruent, you cn conclude tht the opposite sides re prllel then: If both pirs of opposite sides of qudrilterl re prllel, then the qudrilterl is prllelogrm. (OR efinition of Prllelogrm) 9. MT: NO 10. HT nd HT // M efinition of Prllelogrm (Similr to #8) lssify ech figure s specificlly s you cn bsed on the mrkings in the digrm Rectngle Isosceles Trpezoid Qudrilterl Prllelogrm Prllelogrm Squre