Plane and solid geometry . 54 PLANE GEOMETRY Proposition V. Theorem 116, Two triangles are eqitdi if tlve three sides of onearc equal respectively to tJve three sides of the Given A ABC and RST, AB^RS, BC=ST^ and CA = prove A ABC = A RST. Argument 1 Place Arst so that thelongest side RT shall fallupon its equal AC, Rupon A, T upon C, andso that S shall fall oppo-site B. 2. Draw BS, 3. A ABS is isosceles. 4. .•.Z1 = Z2. 5. A BCS is isosceles. 6. .•.Z3 = Z4. 7 Zl-|-Z:3 = , 1. 2. 7. Reasons Any geometric figure maybe moved from one posi-tion to another withoutchange
Plane and solid geometry . 54 PLANE GEOMETRY Proposition V. Theorem 116, Two triangles are eqitdi if tlve three sides of onearc equal respectively to tJve three sides of the Given A ABC and RST, AB^RS, BC=ST^ and CA = prove A ABC = A RST. Argument 1 Place Arst so that thelongest side RT shall fallupon its equal AC, Rupon A, T upon C, andso that S shall fall oppo-site B. 2. Draw BS, 3. A ABS is isosceles. 4. .•.Z1 = Z2. 5. A BCS is isosceles. 6. .•.Z3 = Z4. 7 Zl-|-Z:3 = , 1. 2. 7. Reasons Any geometric figure maybe moved from one posi-tion to another withoutchange of size or shape.§ 54, 14. A str. line may be drawnfrom any one point toany other. § 54, 15. AB = RS, by hyp. The base A of an isoscelesA are equal. § 111, BC=ST, by hyp. Same reason as 4. If equals are added toequals, the sums areequal. § 54, 2. BOOK I 8£ Argument 8. /. Z J5(7=Z CSA. 9. .*. A ABC = A CSA, AABC=ARST. Heasoks 8. The whole = the sum oi all its parts. § 54, 11. 9. Two A are equal if twc sides and the included Zof one are equal respec-tively to two sides andthe included Z of theother. § 107. Ex. 81. (a) Prove Prop. Y, using two obtuse tri
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
