Question

ABCD is a square, prove that AC = 2AB?​

Answer 1

Step-by-step explanation:

ABCD is a square and AC is the diagonal.

So, ACD and ABC are the two right angled triangle.

Now,

In ABC, according to Pythagoras theorem .

AC sq. = AB sq. + BC sq.

but, AB = BC ( since all sides of a square area equal)

so,

AC sq. = AB sq. + AB sq.

= 2AB sq.

therefore ,

AC = 2AB.

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Answer 2

Step-by-step explanation:

In the square ABCD, ABC is a triangle.

In triangle ABC,

by Pythagoras theorem,

AB² + BC² = AC²

2 AB² = AC² [AB = BC]

SO, AC = √2AB