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

Step-by-step explanation:

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

To find: Prove that △OCD is an isosceles triangle. And find the angles marked as 1 to 8 without using a protractor.

Solution:

As to draw largest square in A4 sheet,Sheet should be fold breadth wise.

BCPO is a square,its diagonal OC =CD

Thus,

In triangle OCD ; OC= CD

So,OCD is an isosceles triangle.

We know that angle opposite to equal sides are equal.

So,

$\angle CDO = \angle COD \\ \\ \angle 6 = \angle 4 + \angle5$

OC is diagonal,it bisect the angle C

$\angle 2 = \angle 3 = 45°$

By the same way

$\angle 1 = \angle4 = 45°$

$\angle CDO + \angle COD + \angle DOC = 180° \\ \\ \angle CDO + \angle COD + 45° = 180° \\ \\ 2\angle CDO = 135° \\ \\ \angle CDO = 67.5° \\ \\ \angle 6 = 67.5° \\ \\ \angle 4 + \angle 5 = 67.5°$

In Silver Rectangle AOPD,all angles are 90°

$\angle D = 90° \\ \\ \angle D = \angle 7 + \angle 6 = 90° \\ \\ \angle 7 + 67.5° = 90° \\ \\ \angle 7 = 22.5°$

Line DP||AO

So,

$\angle 7 = \angle5 = 22.5° \\ \\ (alternate \: interior \: angle)$

thus,

$\angle 6 = \angle8 = 67.5° \\ \\ (alternate \: interior \: angle)$

Thus

$\angle 7 = \angle5 = 22.5° \\ \\ \angle 6 = \angle8 = 67.5° \\ \\ \angle 1 = \angle2 =\angle 3 = \angle4 = 45°$

Hope it helps you.

To learn more on brainly:

1) When you divide A4 in half, you get two A5 sheets. If you further divide those A5 sheets in half, you get four A6 sheets...

https://brainly.in/question/21364154

Answer 2

∠1=∠2=∠3=∠4=45°

∠1=∠2=∠3=∠4=45°Hope it helps you.