Q. 1 A4.6( 25 Votes )

Construct the fol

Answer :

Construction of angle of 90°


Steps of construction:


Step 1: Draw a ray OA.



Step 2: With its initial point O as center and any radius, draw an arc, cutting OA at C.



Step 3: With center c and same radius (as in step 2) draw an arc cutting arc at D.



Step 4: With D as center and the same radius, draw an arc cutting the arc cutting at E.



Step 5: With D and E as centers and any convenient radius (more than DE). Draw to two arcs intersecting at P.



Step 6: Join OP. Then AOP = 90°



Justification: -


By construction, OC = CD = OD


Therefore, ΔOCD is an equilateral triangle. So, COD = 60°


Again OD = DE = OE


Therefore, ΔODE is also an equilateral triangle. So, DOE = 60°


Since, OP bisects DOE, so POD = 30°.


Now,


AOP = COD + DOP


= 60° + 30°


= 90°


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