Question

EXERCISE 6.1

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

Answer 1

Answer:

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Step-by-step explanation:

The steps of construction to follow:

Step 1: Draw a ray OP.

Then, take O as the center and any radius draw an arc cutting OP at Q.

Step 2: Now, taking Q as the center 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 center draw the arc of radius more than the half of RS and draw two arcs intersecting at A. Then, join OA.

Hence,  ∠POA = 90°

Justification:

We need to justify, ∠POA = 90°

So, join OR and OS and RQ. we obtain

construction 4

By construction OQ = OS = QR.

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

So, ∠SOR = 60°

Now,  ∠ROQ = 60° that means ∠ROP = 60°

Then, join AS and AR:

construction 5

Now, in △OSA and △ORA:

SR = SR  (common)  

AS = AR  (Radii of same arcs)

OS = OR  (radii of the same arcs)

So, ∠SOA = ∠ROA = $\frac{1}{2}$ (∠SOR)

Therefore, ∠ROA = 30°

and ∠POA = ∠ROA +∠POR = 30° +60° =90°

Hence, justified.

Answer 2

Please view the images respectively.

Hope it helps You