 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...equal (Th. XXI.) ; hence all the angles are equal. PROPOSITION XXII. — THEOREM. CONVERSELY. — // two angles of a triangle are equal, the sides opposite them are also equal, and the trian gle is isosceles. Given. — Let ABC be a triangle having the angle A equal to the angle B. To... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...point D on the base AC so that AD > DC. Prove Z ^1Z)B > Z BD C. BOOK I PROPOSITION XXIX. THEOREM 185. If two angles of a triangle are equal, the sides opposite them are equal. Let ABC be a A having ZA = ZC To Prove AB =BC. Proof. Draw BD bisecting ZB Prove &ABD and BDC... | |
 | Alan Sanders - Geometry, Modern - 1901 - 260 pages
...to a point D on the base ^4C so that AD>DC. Prove /-BDC> L. ADB. PROPOSITION XXIX. THEOREM 185. // two angles of a triangle are equal, the sides opposite them are equal. Let ABC be a A having ZA=ZC To Prove AB=BC. Proof. Draw BD bisecting ZB Prove &ABD and BDC mutually... | |
 | American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...the triangle. 84. Corollary II. An equilateral triangle is equiangular. THEOREM XXII. 85. Conversely, if two angles of a triangle are equal, the sides opposite them are equal, and the triangle is isosceles. In the triangle ABC let the angles A and B be equal. To prove... | |
 | Alan Sanders - Geometry - 1903 - 392 pages
...AB equal to BC. To Prove ZA = Z C. [Draw BD to the middle point of AC, and apply § 1126.] CONVERSE. If two angles of a triangle are equal, the sides opposite them are equal. Let ABC have ZA = Z C. To Prove AB = BC. Proof. The polar triangle of ABC has two sides equal.... | |
 | John Alton Avery - Geometry, Modern - 1903 - 136 pages
...ZZ = ZT, and side XY= side RS. To prove A XYZ = A RST. THEOREM XXVII 75. (Converse of Theo. VIII.) If two angles of a triangle are equal, the sides opposite them are equal, and the triangle is isosceles. Hyp. In A ABC, \etZA = ZB. To prove that AC = BC, or that A ABC... | |
 | George Clinton Shutts - Geometry - 1904 - 112 pages
...figure and show this to be true. Show the equality of the As in other cases. BD = B C. 126. Theorem. // two angles of a triangle are equal, the sides opposite them are equal and the triangle is isosceles. B M Let ABC represent a triangle in which the angle B is equal... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...triangles are congruent. 89. In an isosceles triangle the angles opposite the equal sides are equal. 95. If two angles of a triangle are equal, the sides opposite them are equal and the triangle is isosceles. 100. If two triangles have the three sides of one respectively... | |
 | George William Myers - Mathematics - 1909 - 394 pages
...the vertex to the midpoint of the base bisects the vertex-angle, and is perpendicular to the base. 9. If two angles of a triangle are equal, the sides opposite them are equal. In this statement, it is assumed that two angles of a triangle are equal. From this it is inferred... | |
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Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles. 
