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Find the acute angle between two diagonals of quadrilateral ABCD if it is known that AB=BC=CD and AC=BD=AD.

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The Answer is 45 degrees
User Eric Coleman
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2 votes

Answer:

45⁰

Explanation:

The quadrilateral ABCD is a square.

Since the question stated that all the sides are equal. (AB=BC=CD)

It also stated that the diagnonals are equal. (AC=BD=AD)

I wish I could draw to explain this easily

A square has four right angles.

A right angle is a 90⁰ angle.

The diagonals divide each 90⁰ angle by 2

I hope you know what a diagonal is.

It is a line from a corner of the square to the opposite corner. This cuts the square into two equal sides.

After drawing the first diagonal two triangles of equal size will be seen.

After drawing the second diagonal the two triangles that appeared will each be cut into halves.

Now, you'll have four equal triangles.

think of it as a square pizza cut into four slices...

Uh huh , now you understand

User Gdelfino
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