Construct a rhombus PAIR, given that PA = 6 cm and angle ∠A = 110°.
Solution:
Given, PAIR is a rhombus.
PA = 6 cm
∠A = 110°
We have to construct a rhombus PAIR.
A rhombus can be defined as a special parallelogram as it fulfills the requirements of a parallelogram, i.e. a quadrilateral with two pairs of parallel sides.
A rhombus has all four sides equal just like a square. That is why it is also known as a tilted square.
In a rhombus, all the sides are equal.
So, PA = AI = IR = RP = 6 cm
The adjacent angles are always supplementary.
So, ∠A + ∠I = 180°
110° + ∠I = 180°
∠I = 180° - 110°
∠I = 70°
To construct a rhombus PAIR,
(i) Draw a line segment AI = 6 cm
(ii) Draw a ray AX such that ∠IAX = 110°
(iii) Draw a ray IY such that ∠AIY = 70°
(iv) With A and I as centres and radius 6cm draw arcs intersecting AX and IY at P and R.
(v) Join P and R.
Therefore, PAIR is the required rhombus.
✦ Try This: Construct a rhombus ABCD, given that AB = 5 cm and angle ∠A = 80°.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Solved Problem 34
Construct a rhombus PAIR, given that PA = 6 cm and angle ∠A = 110°.
Summary:
A rhombus PAIR, given that PA = 6 cm and angle ∠A = 110° is constructed.
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