Question

1. which of the following statements is false?

10 cm
c1 = 40°
bo = 7.8 cm
ao = 7.8 cm
a2 = 40°

Explanation:

Step1: Recall properties of parallelogram

In a parallelogram, opposite - angles are equal. So, $\angle C=\angle A$ and $\angle D=\angle B$. Also, the diagonals of a parallelogram bisect each other.

Step2: Analyze angle equality

Since opposite angles of a parallelogram are equal, if one of the angles at $C$ is $40^{\circ}$, the opposite - angle at $A$ has a part $a_2 = 40^{\circ}$. And $c_1=40^{\circ}$ as it is part of the angle at $C$.

Step3: Analyze diagonal properties

The diagonals of a parallelogram bisect each other. Given that the length of one part of a diagonal (say $CO = 7.8$ cm), then $AO=7.8$ cm. But $BO$ is not equal to $7.8$ cm. The diagonals of a parallelogram do not have this property that one non - opposite half of the diagonals are equal.

Answer:

BO = 7.8 cm