ABCD rectangular trapezoid with bases AD = 9cm, BC = 4cm, find the length of the AC
| July 10, 2021 | education
ABCD rectangular trapezoid with bases AD = 9cm, BC = 4cm, find the length of the AC diagonal if it is perpendicular to the side of the trapezoid.
Consider the triangles formed by the AC diagonal.
In triangles ABC and ACD, the angles ABC and ACD are straight, and the angle ACD = CAD as criss-crossing angles at the intersection of parallel lines AD and BC secant AC. Then triangles ABC and ACD are similar in the first sign of similarity of right-angled triangles – in an acute angle.
The AC diagonal of the trapezium, in one of the triangles is the hypotenuse, in the other the leg.
AC / AD = BC / AC.
AC * AC = AD * BC.
AC ^ 2 = 9 * 4 = 36.
AC = 6 cm.
Answer: Length AC = 6 cm.
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