Question

no additional details were added for this assignment. view submission quadrilateral abcd is shown in the illustration. prove that abcd is a parallelogram with opposite sides that are congruent. drag and drop the statements to correctly compete the sentence. the coordinates of point c are (a + b, c) ad = bc = ab = dc = the slope of ad and bc is

Explanation:

Step1: Calculate the length of \(AD\) and \(BC\)

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
For \(AD\), \(A(0,0)\) and \(D(b,c)\), so \(AD=\sqrt{(b - 0)^2+(c - 0)^2}=\sqrt{b^{2}+c^{2}}\).
For \(BC\), \(B(a,0)\) and \(C(a + b,c)\), so \(BC=\sqrt{(a + b - a)^2+(c - 0)^2}=\sqrt{b^{2}+c^{2}}\).

Step2: Calculate the length of \(AB\) and \(DC\)

For \(AB\), \(A(0,0)\) and \(B(a,0)\), so \(AB=\sqrt{(a - 0)^2+(0 - 0)^2}=a\).
For \(DC\), \(D(b,c)\) and \(C(a + b,c)\), so \(DC=\sqrt{(a + b - b)^2+(c - c)^2}=a\).

Step3: Calculate the slope of \(\overline{AD}\) and \(\overline{BC}\)

Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
For \(\overline{AD}\), \(m_{AD}=\frac{c - 0}{b - 0}=\frac{c}{b}\).
For \(\overline{BC}\), \(m_{BC}=\frac{c - 0}{(a + b)-a}=\frac{c}{b}\).

Answer:

\(AD = BC=\sqrt{b^{2}+c^{2}}\), \(AB = DC=a\), The slope of \(\overline{AD}\) and \(\overline{BC}\) is \(\frac{c}{b}\)