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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' =... "
Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ... - Σελίδα 380
των Robert Mudie - 1836 - 496 σελίδες
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - 1836 - 496 σελίδες
...greater than the side AD, opposite the less. But E is any point, and wherever it were taken, in u D or D c, AD would still be less than A E. Wherefore,...have not the same ratio as the opposite angles in circuiar measure, yet equal ratios are of course equal. Hence also, if the three sides of a triangle...

The Common School Arithmetic ...

James Stewart Eaton - 1868 - 324 σελίδες
...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,...

The First and Second Books of Euclid, Explained to Beginners

Euclid, C. P. Mason - 1872
...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...

The papers set at the professional preliminary examination

College of preceptors - 1882
...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...

Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - 1895 - 320 σελίδες
...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....

Elements of Geometry

George Cunningham Edwards - 1895 - 293 σελίδες
...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...

Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - 1895 - 320 σελίδες
...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....

Elements of Geometry: Plane and Solid

John Macnie - 1895 - 374 σελίδες
...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...

New Plane Geometry

Wooster Woodruff Beman, David Eugene Smith - 1899 - 252 σελίδες
...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....

Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - 1901 - 440 σελίδες
...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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