Everything Maths Grade 10

Exercise 7 – 4:

1.ABCDis a quadrilateral. DiagonalsACandBDintersect atT.AC=BD,AT=T C,DT=T B.

B C

A D

吀

Prove that:

a)ABCDis a parallelogram

b)ABCDis a rectangle

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Rhombus EMA62

DEFINITION: Rhombus

A rhombus is a parallelogram with all four sides of equal length.

A rhombus has all the properties of a parallelogram:

• Both pairs of opposite sides are parallel.


• Both pairs of opposite sides are equal in length.


• Both pairs of opposite angles are equal.


• Both diagonals bisect each other.

It also has two special properties:

Worked example 6: Special properties of a rhombus

QUESTION

XY ZTis a rhombus. Prove that:

1.the diagonals bisect each other perpendicularly;

2.the diagonals bisect the interior angles.

Z

Y

X

T

伀

R 2

43

21

2

1

12

2

1

SOLUTION

Step 1: Use the definition of a rhombus to fill in on the diagram all equal angles and sides

Step 2: Prove△XT O△ZT O

256 7.3. Quadrilaterals