Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of
(see figure). Show that:
(i)
(ii)
Solution (i)
In
and
, we have
AB=PQ (Given) (1)
AM=PN (Given) (2)
BC=QR (Given)
(But, AM and PN are medians)
(3)
From (1), (2) and (3), we can say that by SSS rule,
Solution (ii)
In
and
, we have
AB=PQ (Given)
(Corresponding parts of congruent triangles (
and
) are equal)
BC=QR (Given)
Therefore, by SAS congruence rule,
.
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