ABCD is a trapezoid with bases of 8 cm and 12 cm. K is the point of intersection of the diagonals of the trapezoid
| August 18, 2021 | education
ABCD is a trapezoid with bases of 8 cm and 12 cm. K is the point of intersection of the diagonals of the trapezoid. Find the length of the segment AK if KC = 6 cm.
The angles ∠ВКС and АКD, formed at the intersection of the trapezoid diagonals, are vertical angles, and therefore have the same value. The angles ∠KBC = ∠KDA and ∠KСВ = ∠KAD since the corresponding angles. Thus, we see that these triangles are similar. Let’s find the coefficient of similarity, which is equal to the ratio of similar sides:
k = AD / BC;
k = 12/8 = 1.5.
A similar side of the segment AK is the segment KC. Therefore, to calculate AK, it is necessary to multiply KC by the similarity coefficient:
AK = KC · k;
AK = 6 1.5 = 9 cm.
Answer: the length of the AK segment is 9 cm.
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