In parallelogram ABCD AB = 6cm, AD = 8cm. Point K lies on side BC and CK = 4cm
May 28, 2021 | education
| In parallelogram ABCD AB = 6cm, AD = 8cm. Point K lies on side BC and CK = 4cm, point F lies on side CD and CF = 3cm. Line segment KF crosses out the diagonal AC at point P. Find AP: PC.
Point F of the CD side is its middle, since the opposite side AB = 6 cm, and CF = 3 cm.
Similarly, point K is the middle of the BC side.
Let’s draw a straight line KН parallel to AB and a straight line FM parallel to AD. These segments divide the parallelogram into four parallelograms of equal size.
AO = CO as half of the AC diagonal. OP = CP as half the diagonal of the parallelogram CFOK.
OP = CP = OC / 2 = AO / 2, and since AO = AC / 2, then CP = AC / 4.
Then AR = AC – AC / 4 = 3 * AC / 4.
The ratio AP / PC = (3 * AC / 4) / (AC / 4) = 3.
Answer: AR / PC = 3/1.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.