⁦Parallel lines meeting a plane and parallel projection⁩

⁦In Ukrainian Grade 10 (geometry, section 4) parallel lines meeting a plane α are studied⁩. ⁦If through points B and C of a segment AB that has the point A in common with α parallel lines are drawn, then CC₁ is a midline of triangle ABB₁ and BB_١ = ٢·CC_١⁩.

⁦If AB does not meet α, then AA₁B₁B is a trapezoid and CC₁ (C the midpoint of AB) is its midline⁩: CC_١ = AA_١ + BB_١٢.

⁦Parallel projection⁩: ⁦through every point of a figure F draw a line parallel to a line l that meets the plane α⁩. ⁦The points where these lines meet α form the figure F₁, the parallel projection of F onto α in the direction of l⁩. ⁦F₁ is also called the image of F⁩.

⁦Theorem 1⁩. ⁦The projection of a line is a line, of a segment a segment⁩. ⁦Theorem 2⁩. ⁦The projection of two parallel lines is two parallel lines or one line⁩. ⁦Theorem 3⁩. ⁦The ratio of the projections of segments on one line or on parallel lines equals the ratio of the segments⁩: A_١B_١C_١D_١ = ABCD.