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To prove that LMNO is a rectangle, consider D LNO and D MON.

seg.LN @ seg.MO given seg.LO @ seg.MN opposite sides of a parallelogram and seg.ON @ seg.NO same side

\ D LNO @ D MON ( SSS )

Ð LON @ Ð MNO ( corresponding angles of congruent triangles ). Since they are interior angles of parallel lines they are supplementary.

\ Ð LON and Ð MNO are both right angles.

\ Ð MNO is a rectangle.


A rhombus is defined as a quadrilateral with all sides congruent. Figure 3.20 shows a rhombus. ABCD where seg.AB @ seg.BC @ seg.CD @ seg.DA. A rhombus has all properties of a parallelogram and some more.

Additional properties of a rhombus

Theorem : The diagonals of a rhombus are perpendicular to each other. Figure 3.20 shows a rhombus ABCD.

Figure 3.22

To prove that seg.AC is perpendicular to seg.BD, consider D BOA and D BOC.

seg.BA @ seg.BC definition of rhombus .......................... (1)

Ð ABD @ Ð CDB alternate angles. Ð DBC @ Ð CDB as seg.CD and seg.CB are congruent. Therefore D CBD is isosceles .

\ Ð ABD @ Ð DBC which is the same as Ð ABO @ Ð CBO ................. (2)

seg.BO @ seg.BO same side .......................... (3)


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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