Question

select the correct answer from each drop - down menu.
consider parallelogram abcd, where ( mangle abc = 135^{circ} ) and the length of diagonal ac is 41 units.

use the figure and given information to complete the statements.
( mangle bcd=square )
the length of segment cd is ( square ) units
the length of segment ae is ( square ) units.

Explanation:

Step1: Find \(m\angle BCD\)

In a parallelogram \(ABCD\), \(AB\parallel CD\). So, \(\angle ABC+\angle BCD = 180^{\circ}\) (consecutive - interior angles). Given \(\angle ABC=135^{\circ}\), then \(\angle BCD=180 - 135=45^{\circ}\).

Step2: Find the length of \(CD\)

In a parallelogram \(ABCD\), \(AB = CD\). Given \(AB = 7\) units, so \(CD = 7\) units.

Step3: Find the length of \(AE\)

In a parallelogram, the diagonals bisect each other. If the length of diagonal \(AC = 41\) units, and \(AE=\frac{1}{2}AC\) (diagonals of a parallelogram bisect each other). So, \(AE=\frac{41}{2}=20.5\) units.

Answer:

\(m\angle BCD = 45\), the length of segment \(CD\) is \(7\) units, the length of segment \(AE\) is \(20.5\) units.