Question

Draw parallelogram ABCD with the following data:
AB = 6 cm, AD = 5 cm and ∠DAB = 45^o.
Let AC and DB meet in O and let E be the mid-point of BC. Join OE.
Prove that:
(i) OE // AB
(ii) OE = `1/2` AB.

Answer 1

To draw the parallelogram follows the steps:
1. First, draw a line AB of measure 6cm. Then draw an angle of measure 45° at point A such that ∠DAB = 45° and AD = 5cm.

2. Now draw a line CD parallel to the line AB of measure 6cm. Then join BC to construct the parallelogram as shown below: 

3. Now it is given that E is the mid-point of BC. We join OE. Now we are to prove that OE || AB and  OE = `1/2` AB.

4. Since O is the mid-point of AC and E is the midpoint of BC, therefore the line is parallel to AB and  OE = `1/2` AB