Plane and solid geometry . latter. Ex. 318. If the lower base KT of trapezoid BSTK is double theupper base B8^ and the diagonals intersect at 0, prove OK double OS,and or double OB, Ex. 319. Construct a trapezoid, giv^en the two bases, one diagonal,and one of the non-parallel sides. In the two following exercises prove the properties which require proof,state those which follow by definition, and those which have been provedin the text : Ex. 320. Properties possessed by all trapezoids: (a) Two sides of a trapezoid are parallel. (6) The two angles adjacent to either of the non-parallel sides ar
Plane and solid geometry . latter. Ex. 318. If the lower base KT of trapezoid BSTK is double theupper base B8^ and the diagonals intersect at 0, prove OK double OS,and or double OB, Ex. 319. Construct a trapezoid, giv^en the two bases, one diagonal,and one of the non-parallel sides. In the two following exercises prove the properties which require proof,state those which follow by definition, and those which have been provedin the text : Ex. 320. Properties possessed by all trapezoids: (a) Two sides of a trapezoid are parallel. (6) The two angles adjacent to either of the non-parallel sides aresupplementary. (c) The median of a trapezoid is parallel to the bases and equal to onehalf their sum. Ex 321. In an isosceles trapezoid:(a) The two non-parallel sides are equal. (6) The angles at each base are equal and the opposite angles aresupplementary. (c) The diagonals are equal. Ho PLANE GEOMETRY Pjropositiox XL. Theorem 252. Tlie two perpeivdieulars to the sides of an anglefrom any point in its Msector are B DA Given ZabC] P any point in BE^ the bisector of ZabC\ PDand PEj the Js from P to BA and BC respectively. To prove PD = PE, Argument Only 1. In rt. A DBP and PBE^ PB=PB. 2. Z DBP = Z PBE, 3. .-. A DBP = APBE, 4. .*. PD = PE, 253. Prop. XL may be stated as follows: Every point in the bisector of an angle is equidistant from thesides of the angle, Ex. 322. Find a point in one side of a triangle which is equidistantfrom the other two sides of the triangle. Ex. 323. Find a point equidistant from two given intersecting linesand also at a given distance from a fixed third line. Ex. 324. Find a point equidistant from two given intersecting linesand also equidistant from two given parallel lines. Ex. 325. Find a point equidistant from the four sides of a rhombus. Ex. 326. The two altitudes of a rhombus are equal Prove. Ex. 327. Construct the locus of the center of a circle of given radius,which rolls within a given angle so that it always touches a sid6 of
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
