25 . 4. (3) 7. O 25 . aϽbϽc 234 2.4 5 3c ϭ 15 4 3
26 a, b, c 2 3 2a, 2b, 2c 3a, 3 3, 4, 5 9, 12 152 ϭ 9 225 ϭ 8 9 5, 12, 13 8, 15, 17
3b, 3c 4 2.4 2, 15 4a, 4b, 4c 2.4a, 2.4b, 2.4c 92 ϩ 122 81ϩ144 9, 12, 15
5. 37 6. 6 ϫ8 ϫ24 x 6. 8 ᮀABCD ᮀEF aϩb c
27 12 24 . . FGH ab
28 A a Ib B 2 43 a b1 1 c 2 L7 c c 5 J a c b 4 3 C 6 a DbK 1 1. ᮀABCD ᮀEFGH 2. ᮀEFGH 3. ᮀABCD 4. 5. ᮀIJKL 6. ᮀIJKL 7. ᮀEMQO 8. ᮀPGNQ 9. ᮀIJKL 1. ᮀABCD (aϩb)2 ϭ a2ϩ2abϩ 2. ᮀEFGH (aϩb)2 ϭ a2ϩ2abϩ 3. ᮀABCD ᮀEFGH 4. 5. ᮀIJKL ^1 ϩ ^2 ϭ 90Њ ^1 ϭ ^3 ^3 ϩ ^2 ϭ 90Њ ^3 ϩ ^2 ϩ 4^ ϭ 180 (1) (2) 4^ ϭ 90Њ
E a M bF 7 a a c Q8 OP b c6 b 5 H a N bG 2 ᮀABCD ᮀEFGH c ᮀEMQO ᮀPGNQ ϩb2 ϩb2 H( 1 2) 1 ϫaϫb ϭ 1 ab 22 4^ ϭ 90Њ Њ( ) (⌬AIL Х ⌬BJI) ..........(1) Њ( ) ..........(2) 0Њ ( ) Њ
^5 , ᮀIJKL c ᮀIJKL 6. ᮀIJKL c 7. ᮀEMQO 8. ᮀPGNQ 9. ᮀABCD ᮀEFGH ᮀIJKL ϭ ᮀ c2 ϭ a2ϩb2 1. ᮀABCD c Aa b1c H 5 c a 4 D bG (1) ᮀABCD (aϩb)2 ϭ a2ϩ2abϩ.. (2) ᮀEFGH (3) 4 (4) ᮀABCD (aϩb)2Ϫ4 1 a b ϭ a2ϩ2abϩb2Ϫ 2 ϭ a2ϩ .............. (2) (4) c2 ϭ
29 ^6 ^7 90Њ c2 a2 b2 4 4 ᮀEMQOϩ ᮀPGNQ aϩb ᮀEFGH E bB 2a c 5 c F 3 b a C ................... 4 1 a b ϭ .................... 2 Ϫ.................... ....... a2ϩ ....................
30 2. ᮀABDE DqE pr 3 p C4 2 q B (1) AC^ E 90Њ (2) ⌬ABC (3) ⌬CDE 1 ϫpϫ .................... ϭ (4) ⌬ACE 2 (5) 1 ϫ....................ϫq ϭ 2 1 ϫrϫ .................... ϭ 2 (2), (3) (4) ....................ϩ....................ϩ.................... (6) ᮀABDE 1 ϫ(pϩq)(pϩq) ϭ 1 (p2ϩ2pqϩ ....... 22 (7) (5) (6) pqϩ 1 r2 ϭ 1 p2ϩ 22 r2 ϭ ..........
1 A 1 pq 2 1 pq 2 1 r2 2 ϭ pqϩ 1 r2 2 ..............) ϭ 1 p2ϩpqϩ 1 q2 22 ᮀABDE ϩpqϩ 1 q2 2 ...........ϩ....................
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