Question 1118690
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Let x be the measure of angles DAB and DBC; let y be the measure of angle ADB.<br>
Then since the sum of the measures of angles A and D in the trapezium is 180 degrees, the measure of angle BDC is (180-x-y) degrees.<br>
And in triangle ABD, the measure of angle ABD is also (180-x-y) degrees.<br>
So two angles of triangle ABD are congruent to two angles of triangle BDC, so the third angles are congruent, and triangles ABD and BDC are similar.<br>
Then corresponding parts of similar triangles gives us the desired result:<br>
{{{AB/BD = BD/CD}}}
{{{(BD)^2 = AB*CD}}}
{{{BD = sqrt(AB*CD)}}}