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TEOREMA LUI THALES1) Desenai un segment AB i luai un punct PAB, pentru care:

a) P(AB), b) P(AB),

c) P(AB), d) P(AB),

e) P (AB), f) P (AB),

g) P (AB), h) P (AB),

2) Segmentul MN = 48 cm i P(MN).

a) Dac , aflai lungimea segmentelor MP i NP

b) Dac , aflai lungimea segmentelor MP i NP

c) Dac , aflai lungimea segmentelor MP i NP

3) n triunghiul ABC, MN || BC, (M(AB) i N(AC)). a) Dac AM=2 cm, AB=5 cm, AN=4 cm, aflai lungimea segmentelor MB, NC, AC. b) Dac AB=3,2cm, MB=0,7cm, AC=9,6cm, aflai lungimea segmentelor MA, NA, NC. c) Dac AM = 3cm, MB = 2cm, CN = 4cm, aflai lungimea segmentelor AB,

NA, AC.4) n triunghiul ABC, MN || BC, M(AB i N(AC.

a) Dac AM=12cm, AB=4cm, AN=24cm, aflai lungimea segmentelor MB, AC, NC. b) Dac AM = 9,5 cm, AB = 4,3 cm, AC = 12,9 cm, aflai lungimea segmentelor MB,

NC, AC. c) Dac AM = 7cm, AB = 2cm, CN = 10cm, aflai lungimea segmentelor MB,

CA, AN.5) n triunghiul ABC, MN || BC, M(CA i N(BA.

a) Dac AB=10cm, BN=15cm, AM=4cm, aflai lungimea segmentelor AN, AC, MC. b) Dac AB = 8,4cm, BN = 10,5 cm, AC = 9,6 cm, aflai lungimea segmentelor AN,

AM, MC. c) Dac AC = 6cm, MC = 9cm, AN = 2cm, aflai lungimea segmentelor MA,

AB, BN.6) n triunghiul ABC, construim DE || FG || BC, unde D, F AB i E, G AC. a) Dac AD = 4cm, AF = 10cm, AB = 22cm, EG = 3cm, aflai lungimea segmentelor

DF, FB, AE, AG, GC, AC.

b) Dac AD = 4,2cm, AF = 7,8cm, AB = 17,4cm, AE = 1,4cm, aflai lungimea segmentelor DF, FB, GE, CG, GA, AC.

c) Dac AD = 2cm, AF = 5cm, AB = 14cm, CG = 18cm, aflai lungimea segmentelor DB, FD, FB, AE, AG, AC.

7) n triunghiul ABC cu AB = 10cm, BC = 20cm, AC = 15cm, lum un punct E(AB), cu BE = 4cm. Prin punctul E ducem EF || AC, (F(BC)) i EG || BC, (G(AC)), iar prin F ducem FH || AB, (H(AC)). Aflai lungimea segmentelor AH, HG, GC, EA, FB, AG. 8) n triunghiul ABC lum un punct D(AB) i ducem DE || BC, (E(AC)) i EM || AB,

(M(BC)). Demonstrai c: a) b)

9) n patrulaterul ABCD lum punctul M(AC) i ducem MQ || CD, (Q(AD)) i MP ||

BC, (P(AB)). Demonstrai c PQ || BD.10) n patrulaterul ABCD lum punctul M(AB) i ducem MN || AC, (N(BC)) i MP ||

AD, (P(BD)). Demonstrai c PN || CD.

11) n triunghiul ABC lum punctele M(AB) i N(AC). Cercetai dac MN || BC n

urmtoarele cazuri a) AM=2cm, AB=8cm, AN=3cm, NC=9cm. b) AB=11cm, MB=3cm, AN=12cm, NC=4cm.

c) AB=8,6cm, MB=5,2cm, AN=10,2cm, NC=15,6cm.

d) AM=2,7cm, MB=3,2cm, AC=23cm, AN=10,8cm.

e) AM=2cm, MB=3cm, AC=10cm, NC=6cm. f) AB=7cm, AM=3cm, AN=6cm, NC=9cm._1446568589.unknown

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