...cannot be altered without altering the length of the sides. — Proof. If in any triangle, as ABC, the sides were unchangeable, any alteration of the...in the quadrangle А В С D (Fig. В.), the sides AB and С D are equal, and also the sides AD and В С an; equal, then, by drawing the diagonal AC,...

...point C move in two directions at once, (namely, at right angles to AC, and at right angles to BC,) which is impossible, and therefore the angles cannot...quadrangle is a parallelogram. Proof. If, in the quadrangle ABCD, the sides AB and CD are equal, and also the sides AD and BC are equal, then, by drawing the diagonal...

...a. Hence, the angle « and the side BC are supplements of each other ; their sum is n = 180°. 450. If the three sides of a. triangle are respectively equal to the three sides of another, the two triangles are said to be equilateral with respect to each other. 457. If two triangles on the...

...opposite to these angles are also equal . . (Euc. I. 6) 119 Congruence. C.8. — If the three sides of one triangle are respectively equal to the three sides of another triangle, the two triangles shall be congruent (Euc. I. 8) 120 C.4. — If the hypotenuse and one side of one right-angled...

...all respects. If two angles of a triangle are equal, the sides opposite the equal angles are equal. If the three sides of a triangle are respectively equal to the "ihre* sides of another triangle, the triangles are equal in all respects. The straight line joining...