Question

If ABCD is an A4 sheet and BCPO is the square, prove that △OCD is an isosceles triangle. And find the angles marked as 1 to 8 w

Answer 1

Given :  ABCD is an A4 sheet and BCPO is the square

To Find : prove that △OCD is an isosceles triangle

Solution:

ABCD is an A4 sheet

AB = 297 mm = CD

BC = 210 mm  = AD

BCPO  is a sqaure

hence BC = PO = OB = CP = 210 mm

ABCD is rectangle

Hence ∠B = 90°

in ΔOBC

OC² = OB² + BC²

OC² = 210² + 210²

=> OC² = 2 * 210²

=> OC = √2  * 210

=> OC = 297  

in Δ OCD

OC = OD  = 297

Hence Δ OCD is an isosceles triangle

QED

Hence Proved that △OCD is an isosceles triangle

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