Question

Construct ΔPQR such that QR = 6 cm,∠Q=∠R=60°. Measure the other two sides of the triangle and name the triangle.

Answer 1

Dear Student,

Steps of construction:

1) Draw a line segment of QR of 6 cm.

2 ) Draw an angle of 60° from Q and same as from P with the help of protector or compass.

3) Where both 60° angle line meet mark that point as P.

4) Measure the length of PQ and PR with the help of scale.

You will find that all three lengths are equal and all three angles are equal too.

Thus,ΔPQR is known as Equilateral Triangle.

A rough sketch is attached. Hope it helps you.

Answer 2

From the above rough figure ,

Construction steps :

1 ) Draw QR = 6cm line segment.

2 ) Take Q as a center with some radius

draw an arc which intersects QR at A .

Take A as a center with same radius draw

another arc which intersects first arc .

intersecting point is B.

3 ) Draw QB ray .

4 ) Do the same at R . draw RD ray.

5 ) These two rays intersect at one point ' P '

Triangle PQR formed .

Analysis :

In any triangle sum of the three angles = 180°

In ∆PQR ,

<P + <Q + <R = 180°

<P + 60° + 60° = 180°

<P + 120° = 180°

<P = 180° - 120°

<P = 60°
Therefore ,

<P = <Q = <R = 60°

so , PQ = QR = RQ = 6cm

Above triangle is an equilateral triangle.

I hope this helps you.

: )