Plane and solid geometry . e 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 hypoten
Plane and solid geometry . e 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 respectively to the acute angles of thetriangle. Ex. 220. If from the end of the bisector of the vertex angle of triangle a jierpendicular is dropped upon one of the arms, theperpendicular forms with the base an angle equal to half the vertex angle. BOOK I 77 Proposition XXVII. Theorem 204. TJie sum of the angles of any triangle is two 3. Z1=Z^ Given A ABC, To prove /.A + A ABC + Z (7 = 2 rt. A, Argument Reasons 1. Through B draw DE II AC. 1. Parallel line post. § 179. 2. Z 1 + Z ABC + Z 2 2. The sum of all the A about= 2 rt. Zb a point on one side of a str. line passing throughthat point = 2 rt. A, %m, 3. Alt. int. A of II lines areequal. § = Zc. 4. Same reason as 3. Z^ + + ZC 5. Substituting for A 1 and 2 = 2 rt. A, their equals, A A and C, respectively. 205. Cor. I. In a right tidangle tJie two acute anglesare complementary. 206. Cor. II. Ijv a triangle there can be hut one rightangle or one obtuse angle. 207. Cor. III. If two angles of one triangle are equalrespectively to two angles of another, then the third angleof the first is ecjual to the third angle of the second. 208. Cor. IV. // two right triangles have an acuteangle of one equal to an acute angle of the other, theother acute angles are equal. 78 PLANE GEOMETRY 209. Cor. V. Two right triangles are eq
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