CONGRUENT FIGURES
Figures having same shape and same size
are called CONGRUENT FIGURES
SIMILAR OBJECTS
SIMILAR OBJECTS
Figures whose SHAPE is SAME and size
may or may not be same are similar.
SIMILAR OBJECTS
Figures whose shape is same and size may or may not be same are similar.
SIMILAR OBJECTS
A
B
C
60°
30°
8.5 cm
5 cm
10 cm
A
B
C
60°
30°
17 cm
10 cm
20 cm
P
R
Q
ΔABC
is similar to
ΔPRQ
~
∠A ≅ ∠P
∠B ≅ ∠R
∠C ≅ ∠Q
If
then,
AB
PR
=
BC
QR
=
AC
PQ
=
AB
PR
BC
QR
=
=
AC
PQ
8.5
17
=
1
2
=
1
2
=
1
2
5
10
10
20
Corresponding angles of similar triangles are CONGRUENT.
Corresponding sides of similar triangles are in PROPORTION
Zoom 2×
ΔABC is similar to ΔPQR
A
B
C
4 cm
6 cm
5 cm
80o
30o
70o
A
B
C
8 cm
12 cm
10 cm
80o
30o
70o
R
Q
P
∠A = ∠P
, ∠B = ∠Q
, ∠C = ∠R
Corresponding pairs of similar triangles are equal.
SIDES →
doubled
ANGLES →
?
Corresponding pairs of similar triangles are in proportion.
AB
PQ
=
1
2
BC
QR
=
1
2
AC
PR
=
1
2
AC
PR
BC
QR
=
AB
PQ
=
Q
R
P
ΔABC
~
ΔPQR
∠A = ∠P,
∠B = ∠Q,
∠C = ∠R
A
B
C
A
P
B
C
R
AB
PQ
BC
QR
=
=
AC
PR
Q
Corresponding sides of similar triangles
Corresponding angles of similar triangles
ΔABC
~
ΔQRP
∠A ≅ ∠Q
∠B ≅ ∠R
∠C ≅ ∠P
AB
QR
BC
PR
=
=
AC
PQ
Corresponding sides of similar triangles
Corresponding angles of similar triangles
[Given]
∴
Also,
[c.s.s.t.]
[c.a.s.t.]
SIMILAR TRIANGLES