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" In an isosceles triangle the angles opposite the equal sides are equal. "
Elements of Plane and Solid Geometry - Page 46
by George Albert Wentworth - 1877 - 398 pages
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 460 pages
...third side has also the greater included angle. 80. 9. THEOREMS ON THE PROPERTIES OF TRIANGLES. (1) In an isosceles triangle, the angles opposite the equal sides are equal. 48. (2) The straight line which bisects the vertical angle of an isosceles triangle also bisects...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...angle of the other. 144. Two right triangles are equal if their legs are equal, each to each. 145. In an isosceles triangle the angles opposite the equal sides are equal. 147. If two angles of a triangle are equal, the sides opposite the equal angles are equal, and the...
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Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1903 - 392 pages
...of the other pair of vertical angles. Find the values of the four angles. PROPOSITION X. THEOREM 81. In an isosceles triangle, the angles opposite the equal sides are equal. Let ABC be an isosceles A, having AB = BC. To Prove ZA = /L C. Proof. Draw BD bisecting AC. ( 55.) B...
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Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...=& DEF, Art. 47. (geometric figures which coincide are equal), Qc 1. B. PROPOSITION IX. THEOREM 99. In an isosceles triangle the angles opposite the equal sides are equal, B Given the isosceles A ABC in which AB = BC. To prove ZA - Z C. Proof e Let BD be drawn so as to bisect...
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Solid Geometry

Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...hypotenuse and an acute angle of one are equal to the hypotenuse and. an acute angle of the other. 99. In an isosceles triangle the angles opposite the equal sides are equal. 100. // two angles of a triangle are equal, the sides opposite are equal, and the triangle is isosceles....
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Plane Geometry

Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...ABC= A DEF, (geometric figures which coincide are equal) . Art. 47. Q, ED 'PROPOSITION IX. THEOREM 99. In an isosceles triangle the angles opposite the equal sides are equal. B Given the isosceles A ABC in which AB=BC. To prove ZA = /. C. Proof. Let BD be drawn so as to bisect...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
...always true, just as the converse of a theorem is not always true. PROPOSITION XXII. THEOREM. 145. In an isosceles triangle the angles opposite the equal sides are equal. B Z> C Let ABC be an isosceles triangle, having AB and AC equal. To prove that ZB = Z C. Proof. Suppose...
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Treatise on Elementary Geometry

William Chauvenet - 1905 - 336 pages
...the one are respectively equal to a side and the two adjacent angles of the other. PROPOSITION VIII. In an isosceles triangle the angles opposite the equal sides are equal. Corollary. The straight line bisecting the vertical angle of an isosceles triangle bisects the base,...
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Syllabus of Plane Geometry: (corresponding to Euclid, Book I-VI) ; Prepared ...

Cora Lenore Williams - Geometry - 1905 - 122 pages
...of a triangle to the middle point of the opposite side is called the median to that side. Prop. 3. In an isosceles triangle, the angles opposite the equal sides are equal. Prop. 4. An equilateral triangle is also equiangular. Prop. 5. If two angles of a triangle are equal,...
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Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ...

International Correspondence Schools - Building - 1906 - 620 pages
...equal to the angle C" AD, or to C' A1 B1, and by Art. 74 the triangles CA B and C' A' B' are equal. 76. In an isosceles triangle, the angles opposite the equal sides are equal. Let ABC, Fig. 51, be an isosceles triangle in which AB -B C. Draw the bisector BD of the angle B. Then,...
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