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The three special parallelograms — rhombus, rectangle, and square — room so-called due to the fact that they’re special instances of the parallelogram. (In addition, the square is a special situation or kind of both the rectangle and also the rhombus.)

Here room the properties of the rhombus, rectangle, and square. Note that because these three quadrilaterals are all parallelograms, your properties incorporate the parallel properties.

You are watching: The diagonals of a rectangle are perpendicular

The rhombus has actually the complying with properties:

All that the properties of a parallelogram use (the ones that matter here are parallel sides, opposite angles room congruent, and consecutive angles room supplementary).

All sides room congruent through definition.

The diagonals bisect the angles.

The diagonals space perpendicular bisectors of each other.

The rectangle has the complying with properties:

All that the nature of a parallelogram use (the ones the matter here are parallel sides, the opposite sides room congruent, and also diagonals bisect each other).

All angles are right angles by definition.

The diagonals room congruent.

The square has the following properties:

All of the properties of a rhombus use (the ones that matter right here are parallel sides, diagonals space perpendicular bisectors of each other, and also diagonals bisect the angles).

All of the properties of a rectangle use (the only one that matters right here is diagonals are congruent).

All sides space congruent through definition.

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All angle are appropriate angles through definition.

Now shot working with a problem. Given the rectangle together shown, discover the measures of edge 1 and also angle 2:

Here’s the solution: MNPQ is a rectangle, so edge Q = 90°. Thus, due to the fact that there space 180° in a triangle, you can say