Assignments Ag Chapter 4

Advanced Geometry Assignment Sheet Chapter 4 – Congruent Triangles Don't forget to draw sketches, show your work, and jot down questions!

#22: Applying Triangle Sum Properties (4.1) p. 221 – 224: # 1 – 6, 11 – 19 odds, 21 – 27, 31 – 37 odds, 44 – 47 #23: Apply Congruence and Triangles (4.2) p. 228 – 231: # 3 – 16, 19 – 21 #24: Prove Triangles Congruent by SSS (4.3) p. 236 – 239: # 1 – 7, 11, 16 – 19, 21, 34 – 36 #25: Prove Triangles Congruent by SAS & HL (4.4) p. 243 – 246: # 3 – 19 odds, 20 – 22, 25, 27, 30, 39 #26: Review for Quiz Worksheet #27: Prove Triangles Congruent by ASA & AAS (4.5) p. 252 – 255: # 3 – 5, 7 – 10, 12, 14 – 20, 37 – 43 odds #28: Use Congruent Triangles (4.6) p. 259 – 263: # 3 – 9, 13 – 20, 27, 28, 31, 33 – 35 #29: Isosceles & Equilateral Triangles (4.7) p. 267 – 270: # 3 – 29 odds, 32 – 33, 46 – 48 #30: Chapter Review p. 282 – 285: #1 – 26

Chapter 4 – Additional Answers #22 2)E 4)A 6)D 22) 130 24) 130 26) 30 44) 115 46) 130

S G and S O , S H & S R , S K & S T , S J & S S , GH & QR , HJ & RS , JK & ST , KG & TQ. Sample answer HJKG  RSTQ 6) 33˚ 8) NL 10) ΔNML 12) The triangles cannot be proved congruent. 14) VWXYZ = KLMNJ or VWXYZ  MLKJN, all corresponding sides and angles are congruent 16) 11 20) 5,2 #23 4)

#24

y

2) neither 4) neither 6) true, SSS 16) B 18) not congruent CA

1  FD 32) 3/5 34) y   x  2 36) 2

1 x  20 2

#25 20) not enough information 22) HL 30) Since

S DAC  S FAB the triangles are congruent by SAS.

S F , S L 10) HG, NM 12) ED  ED by the Reflexive Property of Segment Congruence 14) yes, SAS 16) No, AC and DE are not corresponding sides 18) no 20) no #27 4) no 8)

#28 4) ΔQPR, Δ TPS; SAS 6) ΔCAD, ΔBDA; AAS 8)ΔVRT, ΔQVW; AAS 14) B 16) ΔAEB  ΔDEC BY AAS which makes S ABE  S DCE . Then by the Congruent Supplements Theorem, S 1  S 2 . 18) Show ΔABC  ΔCBE

AE  CE . Use Angle Addition Postulate and congruent angles to show S FAE  DCE. Then ΔAEF  ΔCED by SAS, and S 1  S 2. 20) Since ΔTVY  ΔUXZ by SAS you have YT  ZU . . Since YT || ZU , you have S YTW  S UZW and S TYW  S ZUW by the Alternate Interior Angles Theorem, making ΔTYW  ΔZUW by ASA. Using corresponding parts and vertical angles, you have ΔTWU  ΔZWY by SAS, making S 1  S 2 . 28) Because CD  DE and CD  AC , S D and S C are congruent right angles. The vertical angles S DBE and S CBA are congruent. So, ΔDBE  ΔCBA by ASA. Then because corresponding parts of congruent triangles are congruent, AC  DE . So, you can find the distance AC across the canyon by measuring DE. 34) yes; AE  CE by Corresponding Parts of Congruent Triangles are Congruent, S CEB  S AEB by the Right Angle Congruence Theorem and BE  BE so ΔBAE  ΔBCE. By Corresponding Parts of Congruent Triangles are Congruent, AB  BC . by ASA, which gives you

#29 32) 150; one triangle is equiangular and the other two triangles are congruent making x˚ the measure of the third angle in the center. x+x+60=360. 46) Statements (Reasons) 1.AB  CD,AE  DE, S BAE  S CDB (Given) 2.ΔABE  ΔDCE (SAS) 46b) ΔAED, ΔBEC 46c) S EDA, S EBC, S ECB 46d) No; ΔAED and ΔBEC remain isosceles triangles with S BEC  S AED. 48) Yes; m S ABC=50˚ and m S BAC=50˚. The Converse of Base Angles Theorem guarantees that AC  BC making ΔABC isosceles. #30 2) In an isosceles triangle, base angles are opposite the congruent sides while the congruent sides form the vertex angle. 6) 65˚ 8) 90˚ 10) 15m 12) 50 14) 11 16) not true; BD  CA 18) false; ΔDEF  ΔHGF by HL 20) S D, S G 22) Show ΔFHK and Δ FHG are congruent using HL. S 1 and S 2 will be congruent because corresponding parts of congruent triangles are congruent. 24) 65 26) 1