Question

quadrilateral abcd is a square. find the missing values. bc = m∠dab = ac = m∠aeb = bd = m∠cbd =

Explanation:

Step1: Recall property of square sides

In a square, all sides are equal. Given $AD = 14$, so $BC=14$.

Step2: Recall measure of interior angle of square

Each interior angle of a square is $90^{\circ}$, so $m\angle DAB = 90^{\circ}$.

Step3: Use Pythagorean theorem for diagonal

In right - triangle $ADC$ with $AD = 14$ and $DC = 14$, by Pythagorean theorem $AC=\sqrt{AD^{2}+DC^{2}}=\sqrt{14^{2}+14^{2}}=\sqrt{2\times14^{2}} = 14\sqrt{2}$. Since diagonals of a square are equal, $BD = AC=14\sqrt{2}$.

Step4: Recall property of diagonals of square

The diagonals of a square are perpendicular bisectors of each other, so $m\angle AEB=90^{\circ}$.

Step5: Recall angle - measure in square

The diagonals of a square bisect the angles of the square. So $m\angle CBD = 45^{\circ}$.

Answer:

$BC = 14$
$m\angle DAB=90^{\circ}$
$AC = 14\sqrt{2}$
$m\angle AEB = 90^{\circ}$
$BD = 14\sqrt{2}$
$m\angle CBD=45^{\circ}$