134. The diagonals of a parallelogram bisect each other. Let ABCD be a, and AD, B C, its diagonals. 135. COR.-The diagonals of a rhombus bisect each other = Q. E. D. at right angles. THEOREM XLV. 136. The diagonals of a rectangle are equal. Let ABCD be a rectangle, and AD, B C, its diagonals. 137. COR.-The diagonals of a square are equal and bisect each other at right angles. THEOREM XLVI. 138. If a parallel to the base of a triangle bisects one of the sides, it bisects the other also; and the part of it intercepted between the sides equals half the base. In the ABC, let DE be II to the base AB and bisect AC at D. 139. COR.-The straight line which joins the middle points of two sides of a triangle is parallel to the third side and is equal to half that side. THEOREM XLVII. 140. The parallel to the bases of a trapezoid, bisecting one of the non-parallel sides, bisects the other also. Let ABCD be a trapezoid, AB and DC its bases, E the middle point of AD, and let EF be to AB and DC. Then in the ▲ DBC, BC is bisected at F; EF bisects BC. (138) (138) Q.E. D. 141. COR. The straight line joining the middle points of the non-parallel sides of a trapezoid, is parallel to the base and equals half their sum. |