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Congruence of Triangles
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Hard Questions
Congruence Of Triangles
Maths
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>
In Fig
$7.32$
, measure of some parts of triangles are given. By applying
$RHS$
congruence rule, state which pairs of triangles are congruent. In case of congruent triangles, write the result in symbolic form.
Hard
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For the following congruent triangles, find the pairs of corresponding angles.
Hard
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In the adjacent figure
$ABCD$
is a square and
$ΔAPB$
is an equilateral triangle. Prove that
$ΔAPD≅ΔBPC$
.
(Hint: In
$ΔAPD$
and
$ΔBPCAD=BC,AP=BP$
and
$∠PAD=∠PBC=90_{∘}−60_{∘}=30_{∘})$
Hard
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In fig 3, if AB
$=$
AC and AP
$=$
AQ, then by which congruence criterion
$ΔPBC≅ΔQCB$
A
SSS
B
ASA
C
SAS
D
RHS
Hard
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Given :
EB = DB
AE = BC
$∠A=∠C=90_{∘}$
So,
$ΔABE≅ΔCDB$
Hard
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>
$ABC$
is an isosceles triangle in which
$AC=BCAD$
and
$BE$
are respectively two altitudes of side
$BC$
and
$AC$
. Prove that
$AE=BD$
.
Hard
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>
In the given figure,
$∠BMN=∠CMN$
and AN bisects
$∠BAC$
. Prove that
$ΔABM≡ΔACM$
.
Hard
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>
In the adjacent figure
$ABCD$
is a square and
$ΔAPB$
is an equilateral triangle. Prove that
$ΔAPD≅ΔPPC$
(Hint : In
$ΔAPD$
and
$ΔBPCAD=BC,AP=BP$
and
$∠PAD=∠PBC=90_{∘}−60_{∘}=30_{∘}]$
Hard
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>
In the figure,prove that
$△APM≅△APN$
if
$PM=PN,PM⊥AB$
and
$PN⊥AC$
Hard
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$ABCD$
is a square.
$E$
and
$F$
are respectively the mid-point of
$BC$
and
$CD$
. If
$R$
is the mid point of
$EF$
prove that
$ar(AER)=ar(AFR)$
.
Hard
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>