In trapezoid abcd ac is a diagonal and ∠abc ≅ ∠acd. find ac if the lengths of the bases bc and ad are 14m and 28m respectively.

AC = 14 sqrt(2) = 19.80    

Step-by-step explanation:

Below is the diagram showing you how this has been set up. The figure is a trapezoid which means BC and AD are parallel. AC is a transversal of the parallel lines.

Givens

<ABC = <ACD                          ABCD  is a trapezoidBC = 14AD = 28AC is a transversal of BC and AD

Solution

<ABC = <ACD                Given<DAC = <ACB                Alternate interior angles.ΔACB ≅ΔDAC               AA<BAC = <ADC                Angles of similar triangles are equalAC /28 = 14/AC              Form a proportion from corresponding sidesAC*AC = 14 * 28             Cross multiply the proportion. CombineAC^2 = 392                    Express as prime factors.AC^2 = 7*7*2*2*2           Take the square root of both sidessqrt(AC)^2 = sqrt(7*7*2*2*2) AC = 7*2 * sqrt(2)AC = 14 sqrt(2) = 19.80    

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