Question

If the diagonals of a parallelogram are 12 cm and 16 cm, find the lengths of each segment of the

diagonal into which they are divided. State the property of parallelogram used.​

Answer 1

Answer: 6cm, 8cm

Step-by-step explanation:

Length of each segments of the diagonal are 6cm , 8 cm espectively.

Property Used : Diagonals of a parallelogram bisect each other.

Proof :

Let ABCD be a parallelogram ,where AC and BD are diagonals, intersecting at point O.

AIO : Alternate interior angles

In Δ AOD & ΔBOC,

$\angle 4= \angle 2 \:\:(AIO)$

AD = BC ( Opp. Sides of parallelogram)

$\angle 1=\angle 3\:\:(AIO)$

$\triangle AOD \cong \triangle BOC (ASA)$

Since, corresponding parts of congruent triangles are same.

AO = CO and OD = OB

Hence, we can say diagonals of a parallelogram bisect each other.