Question

Given a parallelogram ABCD. Complete each statement along with the definition or property used.

Answer 1

Properties of parallelogram ABCD are:

(A) Opposite sides of a parallelogram are equal and parallel.

$$\begin{gathered} \mathrm{AB}=\mathrm{DC}\mathrm{and}\mathrm{AB}\parallel \mathrm{DC} \\ \mathrm{AD}=\mathrm{BC}\mathrm{and}\mathrm{AD}\parallel \mathrm{BC} \end{gathered}$$

(B) Opposite angles are equal

$\angle \mathrm{A}=\angle \mathrm{C}\mathrm{and}\angle \mathrm{B}=\angle \mathrm{D}$

(C) Sum of all the angles of a parallelogram is 360.

$\angle \mathrm{A}+\angle \mathrm{B}+\angle \mathrm{C}+\angle \mathrm{D}=360°$

(D) The consecutive angles of a parallelogram are supplementary.

$$\begin{gathered} \angle \mathrm{A}+\angle \mathrm{B}=180° \\ \angle \mathrm{B}+\angle \mathrm{C}=180° \\ \angle \mathrm{C}+\angle \mathrm{D}=180° \\ \angle \mathrm{D}+\angle \mathrm{A}=180° \end{gathered}$$