Plane and solid geometry . elograms. What property dif-ferentiates rectangles from rhomboids (1) by definition ? (2) by proof ?(See Ex. 266 and Ex. 267.) Ex. 302. (a) What two properties that have been proved distinguishsquares from other rectangles ? (See Ex. 277 and Ex. 278.) (5) What two properties that have been proved distinguish rhombusesfrom other rhomboids? (See Ex. 277 and Ex. 278.) (c) Show that the two properties which distinguish squares and rhom-buses from the other members of their class are due to the common prop-erty possessed by squares and rhombuses by definition, Ex. 303. Th
Plane and solid geometry . elograms. What property dif-ferentiates rectangles from rhomboids (1) by definition ? (2) by proof ?(See Ex. 266 and Ex. 267.) Ex. 302. (a) What two properties that have been proved distinguishsquares from other rectangles ? (See Ex. 277 and Ex. 278.) (5) What two properties that have been proved distinguish rhombusesfrom other rhomboids? (See Ex. 277 and Ex. 278.) (c) Show that the two properties which distinguish squares and rhom-buses from the other members of their class are due to the common prop-erty possessed by squares and rhombuses by definition, Ex. 303. The mid-point of the hypotenuse of a right triangle is equi-distant from the three vertices. Ex. 304. If a line AB of given length is moved so that its ends alwaystouch the sides of a given right angle, what is the locus of the mid-pointof AB? 94 PLANE GEOMETRY Proposittox XXXVIII. Theorem 244. If three or more parallel lines intercept equal seg*ments on one transversal, they intercept equal segmentson any otlwr Given II lines AG^ BE, CJ, DK^ etc., which intercept theequal segments AB, BC, CD, etc., on transversal AF, and whichintercept segments GH, HJ, JK, etc., on transversal GL, To prove GH =z EJ == JK, etc. Argument 1. Draw GM, EN, JB, etc. II AF. 2. Now AGMB, BENC, CJBD, etc., are UJ, 3. .-. GM = AB, EN = BC, JR = CD, etc. 4. And AB = BC= CD, etc. 5. .-. GM = EN = JR, etc. 6. Again G3f, EN, JR, etc., are II to each other, 7. .-. Zl = Z2 = Z3, etc. 8. And Z4 = Z5 = Z6, etc. Reasons 1. Parallel line post. § 179. 2. By def. of a O. § 220. 3. The opposite sides of a O are equal. § 232. 4. By hyp. 5. Ax. 1. § 54, 1. 6. If two str. lines are II to a third str. line, they areII to each other. § 180 7. Corresponding A of II lines are equal. § 190. 8. If two A have their sides II right to right and leftto left, they are equal.§ 200, a. BOOK I 95 9. .-. A GHM = A HJN =A JKRj etc. 10. .. GH== HJ = JK, etc. 9. Two A are equal if twoA and the included sideof o
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