Question

Question 1.
Construct a rhombus PAIR, given that PA = 6 cm and angle ∠A = 110°.?????​

Answer 1

According to the property of rhombus,

All the sides of rhombus are congruent.

Now, Side PA = 6. ........(given)

∴ Side PA = Side AI = Side IR = Side RP = 6

Also, the next property of rhombus says that,

The opposite sides of rhombus are congruent.

∴ Hence , L A = L R = 110°

But, we also need to find the measure of its adjacent angles!

So, according to the adjacent angle property of rhombus,

The sum of adjacent sides of rhombus is 180°

Thus, L A + L I = 180°

∴ 110 ° + L I = 180°

∴ L I = 180° - 110°

∴ L I = 70°

Similarly, L P = 70°

Here, we have got all the measures of sides and angles of rhombus. So now it's easy to construct rhombus according to the following steps:

1. Draw horizontal line of 6 cm.
2. Name it as AI
3. On the point A take measure of 110° and draw segment of 6 cm
4. Similarly on I take measure of 110°and draw 6cm line.
5. Joint the above points together and name as P and R.
6. Here's your required rhombus.