Plane and solid geometry . Given A RST with AR^AT,To prove » = f. Argument1. r > ^, T ^;then /.E> Zjf. 3. This is impossible. 4. Next suppose r <^t\ then theZ opposite the less side.§ 156. 3. By hyp., Z /? = Z 21 4. Same reason as 2. 5. Same reason as 3. 6. The two suppositions, r > f and r <ty have beenproved false. 163. Cor. An equiangular triangle is also equilateral. Ex. 155. The bisectors of the base angles of an isosceles triangle forman isosceles trianfjle. BOOK I 57 Proposition XVII. Theorem(Converse of Prop. XV) 164. If two angles of a triangle are unequaly the side
Plane and solid geometry . Given A RST with AR^AT,To prove » = f. Argument1. r > ^, T ^;then /.E> Zjf. 3. This is impossible. 4. Next suppose r <^t\ then theZ opposite the less side.§ 156. 3. By hyp., Z /? = Z 21 4. Same reason as 2. 5. Same reason as 3. 6. The two suppositions, r > f and r <ty have beenproved false. 163. Cor. An equiangular triangle is also equilateral. Ex. 155. The bisectors of the base angles of an isosceles triangle forman isosceles trianfjle. BOOK I 57 Proposition XVII. Theorem(Converse of Prop. XV) 164. If two angles of a triangle are unequaly the sideopposite the greater angle is greater than tlxe side oppositetlie less A b Given A^jBC with Z ^ > Z prove a^ G. Argument 1. a c. 2. First suppose a < c] then Za theZ opposite the less side.§ 156. 3. By hyp., Za> Zc. 4. The base A of an isosceles A are equal. § 111. 5. Same reason as 3. 6. The two suppositions, a <c and a = c, have beerproved false. 165. Cor. The pei^pendieular is the shortest straightline from a point to a line. 166. Def. The length of the perpendicular from a point toa line is called the distance from the point to the line. 58 PLANE GEOMETRY Ex. 156. The sum of the altitudes of any triangle is less than theperimeter of the triangle. Ex. 157. Given the quadrilateral ABCD with B and D right anglesand EC greater than CD. Prove AD greater than AB. Ex.
Size: 2161px × 1156px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
