Construct an angle of 90 degree at the initial point of a given ray and justify the construction.
Answers
Step-by-step explanation:
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.
construction
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.
construction
Hence,
.
Justification:
We need to justify,
So, join OR and OS and RQ. we obtain
construction 4
By construction OQ = OS = QR.
So,
is an equilateral triangle. Similarly
is an equilateral triangle.
So,
Now,
that means
.
Then, join AS and AR:
constructino 5
Now, in triangles OSA and ORA:
(common)
(Radii of same arcs)
(radii of the same arcs)
So,
Therefore,
and
Hence, justified.
Draw the line 7cm .
Make semi circle more than half .
mark the arc .