On the diagonal AC of the parallelogram ABCD, point P is taken, lines BP and CD
| March 1, 2021 | education
On the diagonal AC of the parallelogram ABCD, point P is taken, lines BP and CD intersect at point Q. Find the ratio CQ: DQ if it is known that AP: CP = 3: 7.
In triangles ABP and CPQ, the angle AРB = CPQ as vertical angles, the angle ABP = PQC as criss-crossing angles at the intersection of parallel AB and CQ secant BQ.
Then the triangles are similar in two angles. Then AB / CQ = AP / CP = 3/7.
Since SD = AB, then SD / CQ = 3/7.
SD = CQ – DQ.
3 * CQ = 7 * CQ – 7 * DQ.
7 * DQ = 4 * CQ.
CQ / DQ = 7/4.
Answer: The ratio CQ / DQ = 7/4.
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