Q1. Construct an angle of 90o at the initial point of a given ray and justify the construction.
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.
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.
Now, that means .
Then, join AS and AR:
Now, in triangles OSA and ORA:
(Radii of same arcs)
(radii of the same arcs)
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