Given triangle are similar. In given figure which similarity criterion is used:10. In adjoining figure , if PQ// BC, then the value of QC will be
Answers
Answer:
( i )
In △ABC and △PQR
∠A=∠P,
∠B=∠Q,
∠C=∠R,
∴ By AAA criterion of similarity, △ABC∼△PQR
( ii )
In △ABC and △QRP
QR
AB
=
RP
BC
=
QP
AC
=
2
1
∴ By SSS criterion of similarity, △ABC∼△QRP
( iii )
In △LMP and △DEF
DE
LM
=
4
2.7
,
DF
LP
=
2
1
The sides are not in the equal ratios, Hence the two triangles are not similar.
( iv )
In △MNL and △QPR
∠M=∠Q,
QP
MN
=
QR
ML
=
2
1
∴ By SAS criterion of similarity, △MNL∼△QPR
( v )
In △ABC and △EFD
∠A=∠F,
FD
AB
=
FD
BC
=
2
1
∴ By SAS criterion of similarity, △ABC∼△EFD
( vi )
In △DEF and △PQR
Since, sum of angles of a triangle is 180
o
, Hence, ∠F=30
o
and ∠P=70
o
∠D=∠P,
∠E=∠Q,
∠F=∠R,
∴ By AAA criterion of similarity, △DEF∼△PQR
( i )
In △ABC and △PQR
∠A=∠P,
∠B=∠Q,
∠C=∠R,
∴ By AAA criterion of similarity, △ABC∼△PQR
( ii )
In △ABC and △QRP
QR
AB
=
RP
BC
=
QP
AC
=
2
1
∴ By SSS criterion of similarity, △ABC∼△QRP
( iii )
In △LMP and △DEF
DE
LM
=
4
2.7
,
DF
LP
=
2
1
The sides are not in the equal ratios, Hence the two triangles are not similar.
( iv )
In △MNL and △QPR
∠M=∠Q,
QP
MN
=
QR
ML
=
2
1
∴ By SAS criterion of similarity, △MNL∼△QPR
( v )
In △ABC and △EFD
∠A=∠F,
FD
AB
=
FD
BC
=
2
1
∴ By SAS criterion of similarity, △ABC∼△EFD
( vi )
In △DEF and △PQR
Since, sum of angles of a triangle is 180
o
, Hence, ∠F=30
o
and ∠P=70
o
∠D=∠P,
∠E=∠Q,
∠F=∠R,
∴ By AAA criterion of similarity, △DEF∼△PQR