In an isosceles trapezoid ABCD, the bases are 5 and 13 cm. Diagonal BD is perpendicular to the lateral
| May 8, 2021 | education
In an isosceles trapezoid ABCD, the bases are 5 and 13 cm. Diagonal BD is perpendicular to the lateral side AB, CK is perpendicular to BD (point K belongs to BD). Find BK: KD.
Consider triangles ABD and BCK.
Since the diagonal BD is perpendicular to AB, and the CK is perpendicular to BD, the triangles are rectangular. Angle ВСК = АDВ as crossing, then triangles ВСК and АD are similar in acute angle.
In similar triangles BC / AD = BK / BD = 5/13.
BD = BK + DK.
BK / (BK + DK) = 5/13.
5 * BK + 5 * DK = 13 * BK.
5 * DK = 8 * BK.
BK / DK = 5/8.
Answer: BK / DK = 5/8.
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