Everything Maths Grade 10

In△XAMand△ZCO

XAM^ =ZCO^ (given:△CDZ△ABX)

AXM^ =CZO^ (proved above)

AX =CZ (proved above)

)△XAM △ZCO (AAS)

)M^ 1 =O^ 1

butM^ 1 =M^ 2 (vert opp\s=)

andO^ 1 =O^ 2 (vert opp\s=)

)M^ 2 =O^ 2

Step 3: Similarly, we can show thatN^ 2 =P^ 2

First show△ADW△CBY. Then show△P DW△N BY.

Step 4: Conclusion

Both pairs of opposite angles ofM N OPare equal. ThereforeM N OPis a parallelogram.

VISIT:

This video shows how to prove that the opposite angles of a parallelogram are equal.

See video:2GQNatwww.everythingmaths.co.za

Exercise 12 – 1:

1.In the diagram below,ACandEFbisect each other atG.Eis the midpoint ofAD, andFis the midpoint

ofBC.

a)ProveAECFis a parallelogram.

A

B C

E D

F

:

b)ProveABCDis a parallelogram.

2.ParallelogramABCDandBEF Care shown below. ProveAD=EF.



6

C

.

"

1

3.In the diagram belowP QRSis a parallelogram withP Q=T Q. ProveQ^ 1 =R^

Chapter 12. Euclidean geometry 405