Similar triangles are triangles that have the same shape but different sizes. Triangles are similar if the ratios of corresponding sides are equal, or if their angles are congruent based on the AAA, AA, SAS, or SSS similarity postulates/theorems. Right triangles are similar if the ratios of corresponding legs or a leg and hypotenuse are equal, according to the LL or HL similarity theorems.

1. WELCOME

2. SAMBHU RAJ PR
B.Ed Mathematics
Reg.No.
BADHIRIYA B.Ed Training College
velichikkala

3. Similar Triangles

4. Similar Triangles
Similar Triangles are the exact same shape but
are different sizes
ABC ~ DEF
65
75
75
65 40
DA
C
B
12 cm
10 cm
16 cm
F
E
6 cm
5 cm 8 cm

5. Determining Similar Triangles
= = 2
= = 2
= =2
The ratios of the matching sides are all
the same value(=2). This prove the
Triangles are similar
C
650
750750750
650 400
12 cm 6 cm
750
650
400
A B
E
D F
AB
DE
10
5
BC
EF
16
8
AC
DF
12
6

6. The AAA Similarity Postulate
If three angles of one triangle are congruent to
three angles of another triangle , then the
triangles are similar.
If <A = <D , <B=<E and <C = <F . Then ABC DEF
A
C
B
E
D F
~ ~ ~
~

7. The AA Similarity Postulate
If < A = <D , and <B = <E ,
Then ABC DEF~
~ ~
A
B
C
E
FD

8. The SAS Similarity Theorem
If two sides of one triangle are proportional to
the corresponding two sides of another triangle
and their respective included angles are
congruent , then the triangles are similar .
If and <A = <D
Then ABC DEF~
~
A
B
C D
E
F
AB
DE
AC
DF
=

9. The SSS Similarity Theorem
If the sides of one triangle are proportional to
the corresponding sides of a second triangle ,
then the triangles are similar.

10. Similar Right Triangles
The L-L Similarity Theorem
If the legs of a right triangle are proportional
to the corresponding legs of another right
triangle , the right triangles are similar.

11. The L-L Similarity Theorem
If <C and <F are right angles and =
Then ABC DEF
B
C A
E
F D
~
AB
DE
AC
DF

12. Similar Right Triangles
The H- L Similarity Theorem
If the hypotenuse and leg of a right triangle
are proportional to the corresponding
hypotenuse and leg of another right triangle ,
then the right triangles are similar.

13. The H- L Similarity Theorem
If <C and <F are right angles and =
Then ABC ~ DEF
AB
DE
AC
DF
C
B
A F D
E

14. THANK YOU