Congruencia de triángulos

www.RecursosDidacticos.org

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[pic 2][pic 3]

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•    CASOS DE CONGRUENCIA

• TERCER  CASO    (LLL)

Es cuando se tiene los tres lados congruentes.

[pic 6][pic 7]

Si:         AB         =        PQ

        BC         =        QR                ∆ABC        ≅ ∆PQR

        AC        =        PR

[pic 8][pic 9][pic 10]

[pic 11][pic 12]

                     NOTA

Cuando dos figuras son:

EJERCICIOS DE APLICACIÓN

1. Calcular “x”

a) α[pic 13][pic 14][pic 15]

b) β[pic 16][pic 17][pic 18]

c) θ

d) α + β[pic 19]

e) α + θ

1. Calcular “x” [pic 20]

[pic 21][pic 22][pic 23][pic 24][pic 25][pic 26][pic 27]

a) 37[pic 28][pic 29]

b) 74[pic 30][pic 31]

c)69[pic 32][pic 33]

d) 111

e) 106

[pic 34][pic 35]

[pic 36]

1. Calcular “x”

[pic 37][pic 38][pic 39][pic 40][pic 41][pic 42][pic 43]

a) 80

b) 20[pic 44][pic 45]

c) 50

d) 30[pic 46][pic 47]

e) 10[pic 48]

1. Calcular “x”

[pic 49][pic 50][pic 51]

a) 130

b) 120[pic 52][pic 53][pic 54][pic 55]

c) 110[pic 56][pic 57][pic 58][pic 59]

d) 100[pic 60][pic 61]

e) 90

1. Calcular “x” [pic 62][pic 63]

[pic 64][pic 65][pic 66]

a) 100[pic 67]

b) 80[pic 68][pic 69][pic 70][pic 71][pic 72]

c) 20[pic 73]

d) 50[pic 74][pic 75]

e) 30

1. Calcular “x” [pic 76]

[pic 77]

a) 90[pic 78][pic 79][pic 80][pic 81]

b) 143[pic 82][pic 83]

c) 127[pic 84][pic 85][pic 86]

d) 120[pic 87][pic 88][pic 89][pic 90]

e) 108[pic 91]

1. Calcular : m∢ABC[pic 92]

[pic 93][pic 94][pic 95]

a) 140[pic 96][pic 97][pic 98][pic 99]

b) 130[pic 100]

c) 150[pic 101][pic 102]

d) 120[pic 103][pic 104][pic 105][pic 106][pic 107]

e) 160[pic 108][pic 109]

1. Calcular “x” [pic 110][pic 111][pic 112][pic 113][pic 114]

[pic 115][pic 116]

a) 80[pic 117][pic 118][pic 119]

b) 40[pic 120][pic 121][pic 122][pic 123]

c) 50[pic 124][pic 125]

d) 60[pic 126]

e) 70

1. Calcular “x” [pic 127]

[pic 128][pic 129]

a) 50[pic 130]

b) 40[pic 131][pic 132]

c) 20[pic 133]

d) 80[pic 134][pic 135]

e) 60[pic 136]

1. Calcular “x” [pic 137]

a) 60

b) 70                                                  

c) 80

d) 75

e) 90

1. Calcular “α”

a) 20[pic 138][pic 139][pic 140][pic 141]

b) 40[pic 142][pic 143]

c) 80[pic 144][pic 145][pic 146][pic 147]

d) 60[pic 148][pic 149][pic 150][pic 151]

e) 10[pic 152][pic 153]

1. Calcular “x” ;  α + β = 130

[pic 154][pic 155]

a) 140[pic 156]

b) 130[pic 157][pic 158][pic 159]

c) 120[pic 160][pic 161][pic 162][pic 163]

d) 150[pic 164][pic 165][pic 166]

e) 90[pic 167][pic 168][pic 169][pic 170]

[pic 171]

1. Calcular “x”

a) 50

b) 30

c) 80

d) 100

e) 40

1. Calcular “x”

a) 80[pic 172][pic 173][pic 174][pic 175]

b) 100[pic 176]

c) 60[pic 177][pic 178][pic 179][pic 180]

d) 120[pic 181][pic 182]

e) 90[pic 183][pic 184]

[pic 185][pic 186][pic 187]

1. Calcular “α”

[pic 188][pic 189]

a) 61[pic 190][pic 191][pic 192][pic 193]

b) 71[pic 194][pic 195]

c) 81[pic 196][pic 197]

d) 91[pic 198]

e) 51

[pic 199]

[pic 200]

[pic 201]

TAREA DOMICILIARIA

1. Calcular: [pic 202][pic 203]

[pic 204][pic 205]

a) 30[pic 206][pic 207][pic 208]

b) -30[pic 209]

c) 20[pic 210][pic 211][pic 212][pic 213][pic 214]

d) 40[pic 215]

...