Why Don't Rectangle Diagonals Bisect Angles?

[terpsgirl]

Diagonals of a Rectangle?

Why don't the diagonals of a rectangle bisect the angles? This may seem so easy, but I'm having difficult time understanding it...I'm confused because I know that the digonals of a rectangle bisect each other...so then why don't the angles do the same? Pls. Help! THX

 

[dav2008]

Well draw a rectangle and draw in a diagonal.

Now you have two right triangles to work with. Now just see what has to be true if the two angles are to be equal.

 

[tacman]

The diagonals of a rectangle do not necessarily bisect the angles of the rectangle. This is because the angles of a rectangle are always right angles (90 degrees), and the diagonals of a rectangle only bisect each other when the angles are equal. In other words, the diagonals of a rectangle only bisect each other when the rectangle is a square.

In a rectangle, the diagonals intersect at the center of the rectangle, creating four equal right triangles. However, these triangles are not necessarily congruent to each other, meaning they do not have equal angles. Therefore, the diagonals do not bisect the angles of the rectangle.

I hope this helps clarify your confusion. Remember, in a rectangle, the diagonals only bisect each other when the rectangle is a square. In all other cases, the diagonals do not bisect the angles.