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3.7 Square, Rectangle and Rhombus

These are special cases of parallelogram. Hence they have all the properties of a parallelogram and some additional properties.

Rectangle

A parallelogram in which each angle is 900 is called a rectangle. Hence a rectangle has all the properties of a parallelogram.

1) The opposite sides are parallel and congruent.

2) Diagonals bisect each other.

Apart from these the rectangle has one salient property.

Theorem: The diagonals of a rectangle are congruent. Figure 3.20 shows a rectangle.

Figure 3.20

To prove that seg.AC @ seg.BD consider D ACD and D BDC . Both are right triangles.

seg.AD @ seg.BC by definition

seg.DC @ seg.CD same side

Ð ADC @ Ð BCD - both are right angles.

\D ACD @ D BDC ( SAS )

Therefore, AC @ BD corresponding sides of congruent triangles are congruent. Therefore, the diagonals of a rectangle are congruent The converse of this theorem is used as a test for rectangle.

Theorem: A parallelogram is a rectangle, if its diagonals are congruent. Figure 3.21 shows a parallelogram LMNO whose diagonals are congruent.

Figure 3.21

Index

3. 1 Definition
3. 2 Terminology
3. 3 Sum Of Interior Angles Of A Polygon
3. 4 Sum Of Exterior Angles Of A Polygon
3. 5 Trapezoids
3. 6 Parallelogram
3. 7 Square, Rectangle And Rhombus

Chapter 4

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