Question

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.

Answer 1

AC = 14 sqrt(2) = 19.80

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 trapezoid
• BC = 14
• AD = 28
• AC 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 equal
• AC /28 = 14/AC Form a proportion from corresponding sides
• AC*AC = 14 * 28 Cross multiply the proportion. Combine
• AC^2 = 392 Express as prime factors.
• AC^2 = 7*7*2*2*2 Take the square root of both sides
• sqrt(AC)^2 = sqrt(7*7*2*2*2)
• AC = 7*2 * sqrt(2)
• AC = 14 sqrt(2) = 19.80