 | Robert Mudie - Mathematics - 1836 - 542 pages
...greater than the side AD, opposite the less. But E is any point, and wherever it were taken, in BD or D c, AD would still be less than A E. Wherefore,...have not the same ratio as the opposite angles in circular measure, yet equal ratios are of course equal. Hence also, if the three sides of a triangle... | |
 | James Stewart Eaton - Arithmetic - 1868 - 356 pages
...isosceles triangle are equal to each other, and an equilateral triangle is also equiangular. Conversely, if two angles of a triangle are equal, the sides opposite those angles are equal. 3. A line drawn from the vertex of an equilateral or isosceles triangle, perpendicular to the base,... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...square. See Book I., Prop. 43. 2. The angles at the base of an isosceles triangle are equal. (I. 5.) 3. If two angles of a triangle are equal, the sides opposite those angles are also equal. (I. 6.) 4. If a right line intersect two parallel right lines, the external angle is equal... | |
 | College of preceptors - 1882 - 528 pages
...Explain how you would find out practically, by folding the paper, whether BAD is a right angle or not. 2. If two angles of a triangle are equal, the sides opposite to them are equal. 3. If one side of a triangle is produced, the exterior angle shall be greater than... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...from that point to that line. That this perpendicular is unique will be proved later. 24 Theorem 4. If two angles of a triangle are equal, the sides opposite those angles are equal. Given the A ABC with ZA = Z B. To prove that a = b. Proof. 1. Suppose that aj^b, and that a > b. 2.... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...curved surface (for example, the earth's surface), distance may be measured on a curved line. Theorem 4. If two angles of a triangle are equal, the sides opposite those angles are equal. Given the A ABC with ZA = Z B. To prove that a = b. Proof. 1. Suppose that ap£b, and that a > b. 2.... | |
 | George Cunningham Edwards - Geometry - 1895 - 324 pages
...is solved. QED 4. Solve the same problem, using for the figure an acuteangled trianglei 5. Show that if two angles of a triangle are equal, the sides opposite those angles are equal, ie the triangle will be isosceles. NOTE. A problem is something proposed to be done. The ELEMENTS OF... | |
 | John Macnie - Geometry - 1895 - 386 pages
...position also, so that AB will coincide with A'C', and AC with A'B'. PROPOSITION VII. THEOREM. 65. If two angles of a triangle are equal, the sides opposite those angles are also equal. A' Given: In triangle ABC, angle C equal to angle B ; To Prove : AB is equal to A C. Turn... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...equal, prove that the four lines form two intersecting straight lines. PROPOSITION IV. 69. Theorem. If two angles of a triangle are equal, the sides opposite those angles are equal. AB Given the A ABC with ZA=ZB. To prove that a = b. Proof. 1. Suppose that a =£ b, and that a > b.... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...and is perpendicular to the base. § 49. (3) An equilateral triangle is also equiangular. § ">0. (4) If two angles of a triangle are equal, the sides opposite those angles are also equal. § 51. (5) An equiangular triangle is also equilateral. § 52. (6) If one side of a triangle... | |
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If two angles of a triangle are equal, the sides opposite those angles are equal. AA . . A Given the triangle ABC, in which angle B equals angle C. To prove that AB = A C. Proof. 1. Construct the AA'B'C' congruent to A ABC, by making B'C' = BC, Zfi' =... 
