#### description

- Property: The diagonals of a rectangle are of equal length

#### notes

1) The opposite angles of a rectangle are equal.

2) The opposite sides of a rectangle are parallel to each other.

3) The adjacent angles of a rectangle ae supplementary , and

4) The diagonals of a rectangle bisect each other.

**Property:** The diagonals of a rectangle are of equal length.

**Given :** ABCD is a rectangle. AC and BD are diagonals.**To prove :** AC = BD

ABCD is a rectangle. Therefore it is a parallelogram.

∠A = 90°

AD = BC , ∠A = 90°

AD || BC & AB is transversal.

∠A + ∠B = 180° ..(interior angles)

90° + ∠B = 180°

∠B = 90°

In ∆ ABC & ∆ ABD,

AB = AB ..(common)

∆ ABC ≅ ∆ ABD , ...(SAS rule )

#### Shaalaa.com | Property: The diagonals of a rectangle are of equal length.

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