...angle ABD, respectively equal to the two sides BC, BD, and the included angle DBC; and the angle A will be equal to C. 56. Corollary. An equilateral...the angle B, at the vertex of an isosceles triangle, Js perpendicular to the base-,- and bisects the base. ... Demonstration, a. For, on account of the...

...angle ABD, respectively equal to the two sides BC, BD, and the included angle DBC ; and the angle A will be equal to C. 56. Corollary. An equilateral...Theorem. The line BD (fig. 32), which bisects the angle jB, at the vertex of an isosceles triangle, is perpendicular to the base, and bisects the base. Proof....

...identical, aADB xx aADC ? AD !| BC? 25. And BD xx DC ? COR. n. A straight line bisecting the angle at the vertex of an isosceles triangle is perpendicular to the base and bisects it. PROPOSITION X. § 77. Given, any triangle ABC. Required, any one side aw the sum of the other two....

...angle ABD, respectively equal to the two sides BC, BD, and the included angle DEC ; and the angle A will be equal to C. 56. Corollary. An equilateral...account of the equality of the triangles ABD and BCD, AB must be equal to DC. b. Moreover, the angles BDA and BDC are equal, and are therefore right angles...

...angle ABD, respectively equal to the two sides BC, BD, and the included angle DBC; and the angle A will be equal to C. 56. Corollary. An equilateral...is perpendicular to the base, and bisects the base. Pruof. a. For, on account of the equality of the triangles ABD and BCD, AD must be equal to DC. b....

...angle ABD, respectively equal to the two sides BC, BD, and the included angle DBC; and the angle A will be equal to C. 56. Corollary. An equilateral...equiangular. 57. Theorem. The line BD (fig. 32), which bi-. sects the angle B, at the vertex of an isosceles triangle, is perpendicular to the base, and bisects...

...ADB = ADC, c and BAD = CAD ; that is, the straight line joining the vertex and the middle of the base of an isosceles triangle is perpendicular to the base and bisects the vertical angle. Hence, also, the straight line which bisects the vertical angle of an isosceles triangle...

...= AD C, C and BAD = CAD ; that is, the straight line joining the vertex and the middle of the base of an isosceles triangle is perpendicular to the base and bisects the vertical angle. Hence, also, the straight line which bisects the vertical angle of an isosceles triangle...

...equilateral triangle is also equiangular. 57. Theorem. The line BD (fig. 32), which bi sects the angle /?, at the vertex of an isosceles triangle, is perpendicular...BCD, AD must be equal to DC. b. Moreover, the angles EDA and BDC are equal, and are therefore right angles by the very definition of the right angle in...

...symmetry of the figure. § 64 §61 §180 §182 §179 EXERCISES. 34. The median from the vertex to the base of an isosceles triangle is perpendicular to the base, and bisects the vertical angle. 35. State and prove the converse. 36. The bisector of an exterior angle of an isosceles...