Question

EXERCISE 11.1
1. Construct an angle of 90' at the initial point of a given ray and justify the construction.​

Answer 1

Answer:

Step 1: Draw a ray OP., take O as the centre and any radius draw an arc cutting OP at Q.

Step 2: Now, taking Q as the centre and with the same radius as before draw an arc cutting the previous arc at R. Repeat the process with R to cut the previous arc at S.

Step 3: Take R and S as centre draw the arc of radius more than the half of RS and draw two arcs intersecting at A. Then, join OA.

Hence, angle POA = 90

justify, angle POA = 90

So, join OR and OS and RQ. we obtain

By construction OQ = OS = QR.

So, triangle ROQ is an equilateral triangle. Similarly triangle SOR is an equilateral triangle.

So, angle SOR = 60

Now, angle ROQ = 60 that means angle ROP = 60

Then, join AS and AR:

Now, in triangles OSA and ORA:

SR = SR  (common)  

AS = AR  (Radii of same arcs)

OS = OR  (radii of the same arcs)

So, angle SOA = angle ROA = 1/2 angle SOR

Therefore, angle ROA = 30

and angle POA = angle ROA+angle POR = 30 +60 =90^{\circ}

Hence, justified.