Question

Докажите, что четырёхугольник - ромб, если его вершинами являются середины сторон: а) прямоугольника; б) равнобедренной трапеции.

Answer 1

Б вроде,а может и а вот так что подумай хорошо

Answer 2

The rhombus is a quadrilateral

A rhombus is a special type of quadrilateral where all four sides are of equal length. Therefore, a rhombus is always a quadrilateral.

The midpoints of the sides of a rectangle form a rhombus

Let's consider a rectangle ABCD. The midpoints of its sides are: - Midpoint of AB is E - Midpoint of BC is F - Midpoint of CD is G - Midpoint of DA is H

Since the opposite sides of a rectangle are always equal, EF = FG = GH = HE. Therefore, the figure formed by joining the midpoints E, F, G, H is a rhombus.

The midpoints of the sides of an isosceles trapezoid form a rhombus

Consider an isosceles trapezoid PQRS. The legs PQ and SR are equal by definition of an isosceles trapezoid. The midpoints of its sides are: - Midpoint of PQ is e - Midpoint of QR is f - Midpoint of RS is g - Midpoint of SP is h

Since the legs PQ and SR are equal, and the non-parallel sides QR and RS meet at the midpoint, ef = fg = gh = he. Therefore, the figure formed by joining the midpoints e, f, g, h is a rhombus.