...coincided with the triangle ABD in all its parts. The corollaries to this theorem are : (1.) That the line which bisects the vertical angle of an isosceles triangle, bisects the base, and is perpendicular to it. (2.) That every equilateral triangle is likewise equiangular, (it.) If...

...coincided with the triangle ABD in all its parts. The corollaries to this theorem are : (1.) That the line which bisects the vertical angle of an isosceles triangle, bisects the base, and is perpendicular to it. (3.) That every equilateral triangle is likewise equiangular. (3.) If the...

...and therefore the base and vertical angle are bisected. Cor. 2. It is evident that the right line, which bisects the vertical angle of an isosceles triangle, bisects the base and is perpendicular to it ; and that the right line drawn from the vertical angle, bisecting the....

...respecta (th. 1) ; and consequently the angle л equal to the angle в. af. D. Carol. 1. Hence the line which bisects the vertical angle of an isosceles triangle, bisects the base, and is also perpendicular to it. Carol. 2. Hence too it appears, that every equilateral triangle, is...

...side AC equal to the side BC; then will the angle B be equal to the angle A. — (Fig. ft) The line which bisects the vertical angle of an isosceles triangle, bisects the base, and is also perpendicular to it. Kvery equilateral triangle, is also equiangular, or has all its angles...

...and therefore the base and vertical angle are bisected. Cor. 2. It is evident that the right line, which bisects the vertical angle of an isosceles triangle, bisects the base and is perpendicular to it ; and that the right line drawn from the vertical angle, bisecting the base,...

...of the equal angles А В С, А С В, is equal to two right angles (2.). Cor. 3. The straight line which bisects the vertical angle of an isosceles triangle, bisects the base at right angles : and conversely, the straight line which bisects the base at right angles, passes...

...the category of the figure immediately preceding. SUPPLEMENTARY PROPOSITIONS. 1 . The straight line which bisects the vertical angle of an isosceles triangle, bisects the base, and is perpendicular to it. (Pr. 4.) 2. The straight line which bisects the base of an isosceles triangle,...

...ABC have the side AC equal to the side BC ; then will the angle B be equal to the angle A. The line which bisects the vertical angle of an isosceles triangle, bisects the base, and is also perpendicular to it. Every equilateral triangle, is also equiangular, or has all its angles...

...Geometry of Cape's Course (znd edition), on which the proof chiefly depends. 1 . The straight line which bisects the vertical angle of an isosceles triangle, bisects the base, and is perpendicular to it. (Euclid, i. 4. Cape, i. 6.) 2. The straight line which bisects the base...