In the parallelogram ABCD, side AD = 3cm, diagonal DB = 4cm. Straight BH passes through point
| August 7, 2021 | education
In the parallelogram ABCD, side AD = 3cm, diagonal DB = 4cm. Straight BH passes through point M-midpoint DC and intersects straight line AD at point H. Find DH and CH.
Point M is the middle of DC, then DM = CM. In triangles DНМ and ВСМ the angle DМН = ВМС as vertical angles, the angle МDН = МСВ as criss-crossing angles at the intersection of parallel DH and ВС secant СD. Then the triangles DHM and BCM are equal in side and two adjacent angles, then DH = BC = AD = 3 cm.
In the quadrangle DHSV, the diagonals CD and BH, at point M, are divided in half, then DHSB is a parallelogram, and then CH = BD = 4 cm.
Answer: The length of the segment DH is 3 cm, the length of CH is 4 cm.
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