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Congruent Figures

Congruent Figures. GEOMETRY LESSON 4-1. (For help, go to page 24.). Solve each equation. 1. x + 6 = 25 2. x + 7 + 13 = 33 3. 5 x = 540 4. x + 10 = 2 x 5. For the triangle at the right, use the Triangle Angle-Sum Theorem to find the value of y. 4-1. Congruent Figures.

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Congruent Figures

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  1. Congruent Figures GEOMETRY LESSON 4-1 (For help, go to page 24.) Solve each equation. 1.x + 6 = 25 2.x + 7 + 13 = 33 3. 5x = 540 4.x + 10 = 2x 5. For the triangle at the right, use the Triangle Angle-Sum Theorem to find the value of y. 4-1

  2. Congruent Figures GEOMETRY LESSON 4-1 Solutions 1. Subtract 6 from both sides: x = 19 2. Combine like terms: x + 20 = 33; subtract 20 from both sides: x = 13 3. Divide both sides by 5: x = 108 4. Subtract x from both sides of x + 10 = 2x: 10 = x, or x = 10 5.y + 40 + 90 = 180; combine like terms: y + 130 = 180; subtract 130 from both sides: y = 50 4-1

  3. Angles: A QB TC J Sides: AB QT BC TJ AC QJ Congruent Figures GEOMETRY LESSON 4-1 ABCQTJ. List the congruent corresponding parts. List the corresponding vertices in the same order. List the corresponding sides in the same order. 4-1

  4. Congruent Figures GEOMETRY LESSON 4-1 XYZKLM, mY = 67, and mM = 48. Find mX. Use the Triangle Angle-Sum Theorem and the definition of congruent polygons to find mX. mX + mY + mZ = 180 Triangle Angle-Sum Theorem mZ = mMCorresponding angles of congruent triangles that are congruent mZ = 48 Substitute 48 for mM. mX + 67 + 48 = 180 Substitute. mX + 115 = 180 Simplify. mX = 65 Subtract 115 from each side. 4-1

  5. If ABCCDE, then BACDCE. The diagram above shows BACDEC, not DCE. Corresponding angles are not necessarily congruent, therefore you cannot conclude that ABCCDE. Congruent Figures GEOMETRY LESSON 4-1 Can you conclude that ABCCDE in the figure below? List corresponding vertices in the same order. 4-1

  6. Examine the diagram, and list the congruent corresponding parts for CNG and DNG. a. CGDGGiven b. CNDNGiven c. GNGNReflexive Property of Congruence d. CDGiven e. CNGDNGRight angles are congruent. f. CGNDGNIf two angles of one triangle are congruent to two anglesof another triangle, then the third angles are congruent. (Theorem 4-1.) g. CNGDNGDefinition of triangles Congruent Figures GEOMETRY LESSON 4-1 Show how you can conclude that CNGDNG. List statements and reasons. Congruent triangles have three congruent corresponding sides and three congruent corresponding angles. 4-1

  7. 5.ML 6.B 7.C 8.J 9.KJB 10.CLM 11. JBK 12. MCL Congruent Figures GEOMETRY LESSON 4-1 Pages 182-185 Exercises 1. CABDAB; CD; ABCABD; ACAD; ABAB CBDB 2. GEF JHI; GFE JIH; EGF HJI; GE JH; EF HI FG IJ 3. BK 4.CM 13. E, K, G, N 14.PO SI; OL ID; LY DE; PY SE 15. P S; O I; L D; Y E 16. 33 in. 17. 54 in. 18. 105 19. 77 4-1

  8. s s s s s s s s s s Congruent Figures GEOMETRY LESSON 4-1 20. 36 in. 21. 34 in. 22. 75 23. 103 24. Yes; RTK UTK, RU (Given) RKTUKT If two of a are to two of another , the third are . TRTU, RKUK (Given) TKTK (Reflexive Prop. of ) TRKTUK(Def. of ) 25. No; the corr. sides are not . 26. No; corr. sides are not necessarily . 27. Yes; all corr. sides and are . 28. a. Given b. If || lines, then alt. int. are . c. Given d. If 2 of one are to two of another , then 3rd are . e. Reflexive Prop. of f. Given g. Def. of 4-1

  9. 36. Answers may vary. Sample: It is important that PACHOLDE for the patch to completely fill the hole. 37. Answers may vary. Sample: She could arrange them in a neat pile and pull out the ones of like sizes. 38.JYB XCH 39.BCE ADE 40.TPK TRK 29.A and H; B and G; C and E; D and F 30.x = 15; t = 2 31. 5 32.mA = mD = 20 33.mB = mE = 21 34.BC = EF = 8 35.AC = DF = 19 41.JLM NRZ; JLM ZRN 42. Answers may vary. Sample: The die is a mold that is used to make items that are all the same size. 43. Answers may vary. Sample: TKR MJL: TK MJ; TRML;KRJL;TKRMJL; TRK MLJ;KTRJML Congruent Figures GEOMETRY LESSON 4-1 4-1

  10. 45. Answers may vary. Sample: Since the sum of the of a is 180, and if 2 of one are the same as 2 of a second , then their sum subtracted from 180 has to be the same. 46.KL = 4; LM = 3; KM = 5 47. 2; either (3, 1) or (3, –7) 48. a. 15 b. 44. a. Given b. If || lines, then alt. int. are . c. If || lines, then alt. int. are . d. Vertical are . e. Given f. Given g. Def. of segment bisector h. Def. of s s s s s s s Congruent Figures GEOMETRY LESSON 4-1 4-1

  11. 54. 55. 100         56.RS = PQ 57. 1         58. 12 59. AB GH 49. 1.5 50. 4.25 51. 40 52. 72 53. Answers may vary. Sample: Congruent Figures GEOMETRY LESSON 4-1 4-1

  12. WA NO, AS OT, SH TE, WH NE; W N, A O, S T, H E Sample: DFHZPR Sample: ABDCDB Sample: Two pairs of corresponding sides and two pairs of corresponding angles are given. C A because all right angles are congruent. BDBD by the Reflexive Property of . ABDCDB by the definition of congruent triangles. Congruent Figures GEOMETRY LESSON 4-1 In Exercises 1 and 2, quadrilateral WASH quadrilateral NOTE. 1. List the congruent corresponding parts. 2.mO = mT = 90 and mH = 36. Find mN. 3. Write a statement of triangle congruence.4. Write a statement of triangle congruence.5. Explain your reasoning in Exercise 4 above. 144 4-1

  13. Triangle Congruence by SSS and SAS GEOMETRY LESSON 4-2 (For help, go to Lesson 2-5.) What can you conclude from each diagram? 1.2.3. 4-2

  14. Solutions 1. According to the tick marks on the sides, ABDE. According to the tick marks on the angles, CF. 2. The two triangles share a side, so PRPR. According to the tick marks on the angles, QPR SRP and Q S. 3. According to the tick marks on the sides, TONV. The tick marks on the angles show that MS. Since MO || VS, by the Alternate Interior Angles Theorem MON SVT. Since OVOV by the Reflexive Property, you can use the Segment Addition Property to show TVNO. Triangle Congruence by SSS and SAS GEOMETRY LESSON 4-2 4-2

  15. Given:M is the midpoint of XY, AXAY Prove: AMXAMY Copy the diagram. Mark the congruent sides. You are given that M is the midpoint of XY, and AXAY. Midpoint M implies MXMY. AMAM by the Reflexive Property of Congruence, so AMXAMY by the SSS Postulate. Triangle Congruence by SSS and SAS GEOMETRY LESSON 4-2 Write a paragraph proof. 4-2

  16. It is given that ADBC. Also, DCCD by the Reflexive Property of Congruence. You now have two pairs of corresponding congruent sides. Therefore: Solution 1: If you know ACBD, you can prove ADCBCD by SSS. Solution 2: If you know ADCBCD, you can prove ADCBCD by SAS. Triangle Congruence by SSS and SAS GEOMETRY LESSON 4-2 ADBC. What other information do you need to prove ADCBCD? 4-2

  17. Given: RSGRSH, SGSH From the information given, can you prove RSG RSH? Explain. Copy the diagram. Mark what is given on the diagram. It is given that RSGRSH and SGSH. RSRS by the Reflexive Property of Congruence. Two pairs of corresponding sides and their included angles are congruent, so RSGRSH by the SAS Postulate. Triangle Congruence by SSS and SAS GEOMETRY LESSON 4-2 4-2

  18. Pages 189-192 Exercises 6. Yes; ACDB (Given); AE CE and BE DE (Def. of midpt.); AEB CED (vert. are ) AEBCED by SAS. 7.a. Given b. Reflexive c.JKM d.LMK 8.WV, VU 9.W 1. SSS 2. cannot be proved 3. SAS 4. SSS 5. Yes; OBOB by Refl. Prop.; BOP BOR since all rt. are ; OPOR (Given); the are by SAS. 10.U, V 11.WU 12.X 13.XZ, YZ 14.LG MN 15.TVor RSWU 16.DC CB s s s Triangle Congruence by SSS and SAS GEOMETRY LESSON 4-2 4-2

  19. 17. additional information not needed 18. Yes; ACB EFD by SAS. 19. Yes; PVQSTR by SSS. 20. No; need YVW ZVW or YW ZW. 21. Yes; NMO LOM by SAS. 22.ANGRWT; SAS 23.KLJ MON; SSS 24. Not possible; need HP or DYTK. 25.JEFSVF or JEFSFV; SSS 26.BRT BRS; SSS 27.PQR NMO; SAS 28. No; even though the are , the sides may not be. 29. No; you would need HK or GIJL. 30. yes; SAS 31. s Triangle Congruence by SSS and SAS GEOMETRY LESSON 4-2 4-2

  20. 32. 33. a. Vertical are . b. Given c. Def. of midpt. d. Given e. Def. of midpt. f. SAS 34. Answers may vary. Sample: 35.a–b. Answers may vary. Sample: a. wallpaper designs; ironwork on a bridge; highway warning signs 35. (continued) b. produce a well-balanced, symmetric appearance. In construction, enhance designs. Highway warning signs are more easily identified if they are . 36.ISPPSO; ISPOSPby SAS. 37.IP PO; ISP OSP by SSS. s s s Triangle Congruence by SSS and SAS GEOMETRY LESSON 4-2 4-2

  21. 38. Yes; ADBCBD by SAS; ADB DBC because if || lines, then alt. int. are . 39. Yes; ABC CDA by SAS; DAC ACB because if || lines, then alt. int. are . 40. No; ABCD could be a square with side 5 and EFGH could be a polygon with side 5 but no rt. . 41. 1.FG || KL (Given) 2.GFKFKL (If || lines, then alt. int. are .) 3.FGKL (Given) 4.FKFK (Reflexive Prop. of ) 5.FGK KLF (SAS) 42.AE and BD bisect each other, so ACCE and BCCD. ACBDCE  because vert. are . ACBECD by SAS. s s s s s Triangle Congruence by SSS and SAS GEOMETRY LESSON 4-2 4-2

  22. 45. D 46. G 47. C 48.[2]a.ABAB; Reflexive Prop. of b. No; AB is not a corr. side. [1] one part correct 49.E 50.AB 43. 44.AMMB because M is the midpt. of AB. BAMC because all right are . CMDB is given. AMCMBD by SAS. 51. FG 52.C 53. The product of the slopes of two lines is –1 if and only if the lines are . 54. If x = 2, then 2x = 4. If 2x = 4, then x = 2. 55. If 2x = 6, then x = 3. The statement and the converse are both true. s Triangle Congruence by SSS and SAS GEOMETRY LESSON 4-2 4-2

  23. Triangle Congruence by SSS and SAS GEOMETRY LESSON 4-2 56. If x2 = 9, then x = 3. The statement is true but the converse is false. 4-2

  24. BG and BV APB XPY; SAS If you know DO DG, the triangles are by SSS; if you know DWO DWG, they are by SAS. No; corresponding angles are not between corresponding sides. Triangle Congruence by SSS and SAS GEOMETRY LESSON 4-2 1. In VGB, which sides include B? 2. In STN, which angle is included between NS and TN? 3. Which triangles can you prove congruent? Tell whether you would use the SSS or SAS Postulate. 4. What other information do you need to prove DWODWG? 5. Can you prove SEDBUT from the information given? Explain. N 4-2

  25. Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 (For help, go to the Lesson 4-2.) In JHK, which side is included between the given pair of angles? 1.J and H2.H and K In NLM, which angle is included between the given pair of sides? 3.LN and LM4.NM and LN Give a reason to justify each statement. 5.PRPR6.AD 4-3

  26. Solutions 1.JH 2.HK 3.L 4. N 5. By the Reflexive Property of Congruence, a segment is congruent to itself. 6. By the Triangle Angle-Sum Theorem, the sum of the angles of any triangle is 180. If mC = mF = x and mB = mE = y, then mA = 180 – x – y = mD, so A = D. Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 4-3

  27. The diagram shows NAD and FNCAGD. If F C, thenF C G Therefore, FNI CAT GDO by ASA. Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 Suppose that F is congruent to C and I is not congruent to C. Name the triangles that are congruent by the ASA Postulate. 4-3

  28. It is given that A B and APBP. APX BPY by the Vertical Angles Theorem. Because two pairs of corresponding angles and their included sides are congruent, APXBPY by ASA. Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 Write a paragraph proof. Given: A B, APBP Prove: APXBPY 4-3

  29. Because AB || CD, BAC DCA by the Alternate Interior Angles Theorem. Then ABCCDA if a pair of corresponding sides are congruent. By the Reflexive Property, ACAC soABCCDA by AAS. Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 Write a Plan for Proof that uses AAS. Given: B D, AB || CD Prove: ABCCDA 4-3

  30. 1. B D, AB || CD1. Given 2. BAC DCA2. If lines are ||, then alternate interior angles are . 3. ACCA3. Reflexive Property of Congruence 4. ABCCDA4. AAS Theorem Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 Write a two-column proof that uses AAS. Given: B D, AB || CD Prove: ABCCDA Statements Reasons 4-3

  31. Pages 197-201 Exercises 1.PQR VXW 2.ACBEFD 3.RS 4.N and O 5. yes 6. not possible 7. yes 8. a. Reflexive b. ASA 9. AAS 10. ASA 11. not possible 12.FDE GHI;DFE HGI 13. a.UWV b.UW c. right d. Reflexive 14.B D 15.MU UN 16. PQ QS 17.WZVWZY Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 4-3

  32. 18. a. Vert. are . b. Given c.TQ QR d. AAS 19.PMO NMO; ASA 20.UTS RST; AAS 21.ZVY WVY; AAS 22.TUX DEO; AAS 23. The are not because no sides are . 27. a.SRP b.PR c. alt. int. d.PR e. Reflexive 28. a. Given b. Def. of bis. c. Given d. Reflexive Prop. of e. AAS 24.TXU ODE; ASA 25. The are not because the are not included . 26. Yes; if 2 of a are to 2 of another , then the 3rd are . So, an AAS proof can be rewritten as an ASA proof. s s s s s s s s Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 4-3

  33. 29. a. Def. of b. All right are . c.QTPSTR d. Def. of midpt. e. AAS 30. 34. Yes; by ASA since BDH FDH by def. of bis. and DH DH by the Reflexive Prop. of . 35. Answers may vary. Sample: 36. a. Check students’ work. b. Answers may vary; most likely ASA. 31. Yes; by AAS since MONQOP. 32. Yes; by AAS since FGJHJG because when lines are ||, then alt. int. are and GJGJ by the Reflexive Prop. of . 33. Yes; by ASA, since EAB DBC because || lines have corr. . s s s Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 4-3

  34. 37.AEB CED, BEC DEA, ABC CDA, BAD DCB 38. AEB CED, BEC DEA, ABC CDA, ABD DCA, BAD DCB, ABD DCB, CBA DAB, BCD ADC 39. They are bisectors; ASA. 13 20 40. 41. 42. D 43. F Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 44.[2] a.RPQSPQ,RQP SQP (Def. of bisector) b. ASA [1] one part correct 4-3

  35. 48.AC and CB 49. If corr. are , then the lines are ||. 50. 56 photos 51. 36 photos 52. 60% more paper s s s s s s s s Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 45.[4]a. Def. of midpt. b. Yes; JLM KGM because they are alt. int. of || lines, and LMJGMK because vertical are . So the are by ASA. c. Yes; if two of one are to 2 of another , the third are . [3] incorrect for part b or c, but otherwise correct [2] correct conclusions but incomplete explanations for parts b and c [1] at least one part correct 46.ONLMLN; SAS 47. not possible 4-3

  36. RF GHI PQRAAS ABX ACXAAS Triangle Congruence by ASA and AAS GEOMETRY LESSON 4-3 1. Which side is included between R and F in FTR? 2. Which angles in STU include US? Tell whether you can prove the triangles congruent by ASA or AAS. If you can, state a triangle congruence and the postulate or theorem you used. If not, write not possible. 3. 4. 5. S and U not possible 4-3

  37. Using Congruent Triangles: CPCTC GEOMETRY LESSON 4-4 (For help, go to the Lesson 4-1.) In the diagram, JRCHVG. 1. List the congruent corresponding angles. 2. List the congruent corresponding sides. You are given that TICLOK. 3. List the congruent corresponding angles. 4. List the congruent corresponding sides. 4-4

  38. Using Congruent Triangles: CPCTC GEOMETRY LESSON 4-4 Solutions 1. In the triangle congruence statement, the corresponding vertices are listed in the same order. So, J H, R V, and C G. 2. In the triangle congruence statement, the corresponding vertices are listed in the same order. So, JR HV, RC VG, and JC HG. 3. In the triangle congruence statement, the corresponding vertices are listed in the same order. So, T L, I O, and C K. 4. In the triangle congruence statement, the corresponding vertices are listed in the same order. So, TI LO, IC OK, and TC LK. 4-4

  39. Using Congruent Triangles: CPCTC GEOMETRY LESSON 4-4 What other congruence statements can you prove from the diagram, in which SL SR, and 1 2 are given? SCSC by the Reflexive Property of Congruence, and LSCRSC by SAS. 3 4 by corresponding parts of congruent triangles are congruent. When two triangles are congruent, you can form congruence statements about three pairs of corresponding angles and three pairs of corresponding sides. List the congruence statements. 4-4

  40. Sides: SLSR Given SCSC Reflexive Property of Congruence CLCR Other congruence statement Angles: 1 2 Given 3 4 Corresponding Parts of Congruent Triangles CLS CRS Other congruence statement In the proof, three congruence statements are used, and one congruence statement is proven. That leaves two congruence statements remaining that also can be proved: CLSCRS CLCR Using Congruent Triangles: CPCTC GEOMETRY LESSON 4-4 (continued) 4-4

  41. Using Congruent Triangles: CPCTC GEOMETRY LESSON 4-4 The Given states that DEG and DEF are right angles. What conditions must hold for that to be true? DEG and DEF are the angles the officer makes with the ground. So the officer must stand perpendicular to the ground, and the ground must be level. 4-4

  42. Pages 204-208 Exercises 1.PSQ SPR; SQ RP; PQ SR 2. AAS; ABC EBD; AE; CB DB; DE CA by CPCTC 3. SAS; KLJ OMN; K O; J N; KJ ON by CPCTC 4. SSS; HUG BUG; H B; HUG BUG; UGH UGB by CPCTC 5. They are ; the are by AAS, so all corr. ext. are also . 6. a. SSS b. CPCTC 7.ABDCBD by ASA because BDBD by Reflexive Prop. of ; ABCB by CPCTC. 8.MOEREO by SSS because OE OE by Reflexive Prop. of ; MR by CPCTC. 9.SPT OPT by SAS because TP TP by Reflexive Prop. of ; SO by CPCTC. 10.PNKMNL by SAS because KNP LNM by vert. are ; KPLM by CPCTC. 11.CYTRYP by AAS; CT RP by CPCTC. s s s Using Congruent Triangles: CPCTC GEOMETRY LESSON 4-4 4-4

  43. 12.ATMRMT by SAS because ATM RMT by alt. int. are ; AMT RTM by CPCTC. 13. Yes; ABDCBD by SSS so A C by CPCTC. 14. a. Given b. Given c. Reflexive Prop. of d. AAS 18. The are by SAS so the distance across the sinkhole is 26.5 yd by CPCTC. 19. a. Given b. Def. of c. All right are . d. Given e. Def. of segment bis. f. Reflexive Prop. of g. SAS h. CPCTC s s s s s s s Using Congruent Triangles: CPCTC GEOMETRY LESSON 4-4 15.PKL QKL by def. of bisect, and KL KL by Reflexive Prop. of , so the are by SAS. 16. KLKL by Reflexive Prop. of ; PL LQ by Def. of bis.; KLP KLQ by Def. of ; the are by SAS. 17.KLPKLQ because all rt are ; KLKL by Reflexive Prop. of ; and PKL QKL by def. of bisect; the are by ASA. 4-4

  44. 20. ABXACX by SSS, so BAX CAX by CPCTC. Thus AX bisects BAC by the def. of bisector. 21. Prove ABECDF by SAS since AE FC by subtr. 22. Prove KJMQPM by ASA since PJ and KQ by alt. int. are . 23. e or b, e or b, d, c, f, a 24.BA BC is given; BDBD by the Reflexive Prop. of and since BD bisects ABC, ABD CBD by def. of an bisector; thus, ABD CBD by SAS; ADDC by CPCTC so BD bisects AC by def. of a bis.; ADBCDB by CPCTC and ADB and CDB are suppl.; thus, ADB and CDB are right and BD AC by def. of . 25.a.APPB; ACBC b. The diagram is constructed in such a way that the are by SSS. CPACPB by CPCTC. Since these are and suppl., they are right . Thus, CP is to . s s s s s Using Congruent Triangles: CPCTC GEOMETRY LESSON 4-4 4-4

  45. 26. 1.PR || MG; MP || GR (Given) 2. Draw PG. (2 pts. determine a line.) 3.RPG PGM and RGP GPM (If || lines, then alt. int. are .) 4.PGMGPR (ASA) A similar proof can be written if diagonal RM is drawn. 27. Since PGMGPR (or PMRGRM), then PRMG and MPGR by CPCTC. 28. C 29. C 30. D 31. B 32. C 33.[2] a.KBVKBT; yes; SAS b. CPCTC [1] one part correct 34. ASA 35. AAS s Using Congruent Triangles: CPCTC GEOMETRY LESSON 4-4 4-4

  46. Using Congruent Triangles: CPCTC GEOMETRY LESSON 4-4 36. 95; 85 37. The slope of line m is the same as the slope of line n. 38. not possible 39. not possible 4-4

  47. You are given two pairs of s and AMAM by the Reflexive Prop., so ABM ACM by ASA. AB AC, BM CM, B C You are given a pair of s and a pair of sides and RUQ TUS because vertical angles are , so RUQTUS by AAS. RQ TS, UQ US, R T Using Congruent Triangles: CPCTC GEOMETRY LESSON 4-4 1. What does “CPCTC” stand for? Use the diagram for Exercises 2 and 3. 2. Tell how you would show ABM ACM. 3. Tell what other parts are congruent by CPCTC. Use the diagram for Exercises 4 and 5. 4. Tell how you would show RUQTUS. 5. Tell what other parts are congruent by CPCTC. Corresponding parts of congruent triangles are congruent. 4-4

  48. Isosceles and Equilateral Triangles GEOMETRY LESSON 4-5 (For help, go to the Lesson 3-3.) 1. Name the angle opposite AB. 2. Name the angle opposite BC. 3. Name the side opposite A. 4. Name the side opposite C. 5. Find the value of x. 4-5

  49. Solutions 1. The angle opposite AB is the angle whose side is not AB: C 2. The angle opposite BC is the angle whose side is not BC: A 3. The side opposite A is the side that is not part of A: BC 4. The side opposite C is the side that is not part of C: BA 5. By the Triangle Exterior Angle Theorem, x = 75 + 30 = 105°. Isosceles and Equilateral Triangles GEOMETRY LESSON 4-5 4-5

  50. It is given that XYXZ. By the Reflexive Property of Congruence, XBXB. Isosceles and Equilateral Triangles GEOMETRY LESSON 4-5 Examine the diagram below. Suppose that you draw XBYZ. Can you use SAS to prove XYBXZB? Explain. By the definition of perpendicular, XBY = XBZ. However, because the congruent angles are not included between the congruent corresponding sides, the SAS Postulate does not apply. You cannot prove the triangles congruent using SAS. 4-5

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