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Show that in a right angled triangle, the hypotenuse is the longest side.
BE and CF are two equal altitudes of ∆ABC. Prove that the ∆ABC is isosceles.
In ∆ABC, AD is the perpendicular bisector of BC. Show that ∆ABC is an isosceles triangle
in which AB = AC.
In the figure, AC = AE, AB =
AD and BAD = EAC.
Show that BC = DE.
In the adjoining figure, PR > PQ
and PS bisects QPR. Prove
Two sides AB , BC and median
AM of one triangle ABC are
respectively equal to sides PQ ,
QR and median PN of PQR .
Show that ABC  PQR
In the following figure AB is a
line segment and P is its midpoint. D and E are points on the
same side of AB such that
BAD  ABE and
EPA  DPB . Show that
i) DAP  EBP ii) AD = BE
In the given figure it is given
that AF = AE and BE = CF.
Prove that  ABC is isosceles.
Prove that the angles opposite to equal sides of an isosceles triangle are equal.
10) AD and BC are equal
perpendiculars to a line segment
AB (see Fig.). Show that CD
bisects AB.
11) The land for temple is in the
form of an isosceles triangle 
ABC is in which AB = AC. In
order to make additional
facilities and make the shape still
proper, a donor donated the
adjacent land in such a way tha
the side BA is produced to D
such that AD = AB (see Fig.).
Show that  BCD is a right
angle. What is the value learnt
in this act?
12) ABC and DBC are two isosceles triangles on the same base BC. Show that
ABD = ACD.
13) In an isosceles triangle ABC
with AB = AC, D and E are
points on BC such that BE = CD
(see the figure). Show that AD =
14) In the figure, sides AB and AC
of ABC are extended to points
P and Q respectively. Also,
PBC < QCB. Show that
AC > AB.
15) “Two triangles are congruent if two angles and the included side of one triangle are equal
to two angles and the included side of other triangle” – Prove.