 | Seth Thayer Stewart - Geometry - 1891 - 428 pages
...XIV. 5§1. Theorem Many propositions fire equally true with spherical and plane triangles ; thus, I. In an isosceles triangle, the angles opposite the equal sides are equal. II. If two angles of a triangle are equal, the sides opposite are equal. III. If a triangle is equilateral,... | |
 | Thomas J. Foster - Coal mines and mining - 1891 - 444 pages
...greater side is opposite the greater angle, and the greater angle is opposite the greater side. 7. In an isosceles triangle the angles opposite the equal sides are equal. 8. In any triangle the sum of the three angles is equal to two right angles, or 180°. 9. If two angles... | |
 | George Bruce Halsted - Geometry - 1896 - 208 pages
...axis BD, ^ BDC will fall within 4 ADB, and therefore C must fall between A and B. 224. Corollary I. In an isosceles triangle, the angles opposite the equal sides are equal. 225. Corollary II. If two angles of a triangle are equal, the triangle is isosceles. 226. If we join... | |
 | Education - 1893 - 568 pages
...angle of one are equal, respectively, to two sides and the included angle of the other. 13. Theorem: i. In an isosceles triangle, the angles opposite the equal sides are equal. 2. If two angles of a triangle are equal, the opposite sides are equal, and the triangle is isosceles.... | |
 | Seth Thayer Stewart - Geometry - 1893 - 262 pages
...SPHERICAL TRIANGLES. 5§1. Many propositions are equally true~with spherical and plane triangles ; thus, I. In an isosceles triangle, the angles opposite the equal sides are equal. Draw arc of great О from vertex to middle of base. The two Дs have respectively = sides (hyp. and... | |
 | William Chauvenet - 1893 - 340 pages
...the point D. Hence the triangles coincide throughout, and are equal. PROPOSITION VIII.—THEOREM. 23. In an isosceles triangle the angles opposite the equal sides are equal. Let AB and AC be the equal sides of the isosceles triangle ABC; then the angles B and Care equal. Through... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...HARVARD COLLEGE, June, 1891. In solving problems use fur w the approximate value 3\. 1. Prove that in an isosceles triangle the angles opposite the equal sides are equal to each other. The area of a certain isosceles triangle is 50 square feet and each of its equal sides... | |
 | Adelia Roberts Hornbrook - Geometry - 1895 - 224 pages
...that the equal sides shall coincide, and show the truth of the following theorem : PRINCIPLE 17. — In an isosceles triangle the angles opposite the equal sides are equal. 13. In the isosceles triangle ABC the angle BAC is 70°. How many degrees are there in each exterior... | |
 | Michigan. Department of Public Instruction - Education - 1896 - 710 pages
...altitude of the segment, and R the radius of the sphere. 2. Demonstrate: In an isosceles spherical triangle, the angles opposite the equal sides are equal; and conversely, if two angles of a spherical triangle are equal, the triangle is isosceles. 3. (a) Can there be a spherical triangle whose... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...third side of the first triangle is greater than the angle opposite the third side of the second. 154. In an isosceles triangle the angles opposite the equal sides are equal. 155. Cor. An equilateral triangle is equiangular, and each angle contains 60°. 156. If two angles... | |
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In an isosceles triangle the angles opposite the equal sides are equal. 
