# Q1.    Construct an angle of 90o at the initial point of a given ray and justify the construction.

Answers (1)

The steps of construction to follow:

Step 1: Draw a ray OP.

Then, 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, .

Justification:

We need to justify,

So, join OR and OS and RQ. we obtain

By construction OQ = OS = QR.

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

So,

Now,  that means .

Then, join AS and AR:

Now, in triangles OSA and ORA:

(common)

(Radii of same arcs)

(radii of the same arcs)

So,

Therefore,

and

Hence, justified.

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