Plane and solid geometry . Hence : 200. (a) If two angles have their sides parallel right to rightand left to left, they are equal. (h) If tivo angles have their sides parallel right to left and leftto rights they are supplementary. Ex. 213. In Fig. 3, above, show which is the right side of each of thefour angles about 0. Ex. 214. If a quadrilateral has its opposite sides parallel, its oppositeangles are equal. Ex. 215. Given two equal angles having a side of one parallel to aside of the other, are the other sides necessarily parallel ? Prove. Ex. 216. If two sides of a triangle are parallel r
Plane and solid geometry . Hence : 200. (a) If two angles have their sides parallel right to rightand left to left, they are equal. (h) If tivo angles have their sides parallel right to left and leftto rights they are supplementary. Ex. 213. In Fig. 3, above, show which is the right side of each of thefour angles about 0. Ex. 214. If a quadrilateral has its opposite sides parallel, its oppositeangles are equal. Ex. 215. Given two equal angles having a side of one parallel to aside of the other, are the other sides necessarily parallel ? Prove. Ex. 216. If two sides of a triangle are parallel respectively to twohomologous sides of an equal triangle, right to right and left to left, thethird side of the first is parallel to the third side of the second. Ex. 217. Construct a triangle, given an angle and its bisector andthe altitude drawn from the vertex of the given angle. 76 PLANE GEOMETRY Propositiox XXVI. Theorem 201. Two angles wlwse sides are perpendiczdar, each toeach, are either equal or Given Z.\ and the A at P, with OA ± KC and OB ± ffl). To prove Z1 = Z2=Z3, Zl+Z4=2rt. Zs, Zl+Z5 = 2 rt. A Hint. Draw OEII CiT and OJII BH. Prove 0^± 0^ and OF 1. Z 7 = Z1, and prove Z 7 = Z 2. 202. Note. It will be seen that Zl and Z2, whose sides are ± rightto right (0^ to PAT and left to Left {OB to Pil), are equal; while Zland Z4, whose sides are _L right to left {OA to PC) and left to right{OB to PH), are supplementary. Hence : 203. (a) If two angles have their sides peiyendicular right toright and left to left, they are equal, (h) If two angles have their sides perpendicular right to leftand left to right, they are supplementary. Ex. 218. If from a point outside of an angle perpendiculars aredrawn to the sides of the angle, an angle is formed which is equal to thegiven angle. Ex. 219. In a right triangle if a perpendicular is drawn from thevertex of the right angle to the hypotenuse, the right angle is dividedinto two angles which are equal r
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