maths for class 7

3. 1) Defination of congruency:If two objects have the same
shape, same size and same
measures are called
congruence objects.
Example:-i) Two same
company blade.

4. ii) Biscuits in same packet.
iii) Sheet of same letter-pad.
iv) Toys made of same mould.

5. Sign of congruency:- ~
2)Congruence of lines:-If two
line segments have the same
length, they are congruent.
Also if two line segments are
congruent, they have the same
length.

6. Example:i) AB=2cm
ii) CD=2cm
A 2cm B C 2cm D
3)Congruence of angle:-If two
angles have the same
measures, they are congruent.
Also if two angles are congruent,
their measures are same.

7. Example:-Angle-A & Angle-B
A 30
B 30
Angle-A congruent to
Angle-B.

8. 4) Criterion for congruence of
triangle:• Two triangles are congruent if
the triangle have same
i) Side-Side-Side. {s-s-s}
ii) Side-Angle-Side. {s-A-s}

9. iii) Side-Angle-Angle. {s-A-A}
iv) Right-Hypotenuse-Side. {R-H-S}

10. i) Defination of S-S-S congruence
criterion:-If under a given
criterion:correspondence, the three sides
of one triangle are equal to the
three corresponding sides of
another triangle, then the triangle
are congruent.

11. Example:-
A
3.5cm
5cm
B
7.1cm
P
7.1cm
3.5cm
C
Q
5cm
R

12. So, AB=PR{=3.5cm}
BC=PQ{=7.1cm}
AC=QR{=5cm}
Triangle ABC congruent to
triangle RPQ.

13. ii) Defination of S-A-S
congruence criterion:-If
under a correspondence, two
sides and the angle included
between them of a triangle are
equal to two corresponding
sides and the angle included

14. between them of another
triangle, then the triangles are
congruent.
Example:A
D
7.cm
B
50
7.cm
5.cm
C
E
50
5.cm
F

15. Triangle ABC congruent to
triangle DEF.
So, AB=EF{ 7cm}
BC=DE{5cm}
Angle B= Angle E {50 }

16. iii) Defination of S-A-A
congruence criterion:-If
under a correspondence, two
angles and the included side
of a triangle are equal to two
corresponding angles and the
included side of another

17. triangle, then the triangles are
congruent.
Example:Q
A
B
70
30
3cm
C
R
70
30
3cm
P

18. Triangle ABC is congruent to
triangle QRP.
So, BC=RP{3cm}
Angle B = angle R{ 70 }
Angle C = angle P{30 }

19. iv) Defination of R-H-S
congruence criterion:-If
under a correspondence, the
hypotenuse and one side of a
right-angled triangle are
respectively equal to the
hypotenuse and one side of

20. another right-angled triangle,
then the triangle are
congruent.
Example:A
3cm
B
P
3cm
8cm
C
Q
8cm
R

21. So, Angle B= angle Q{=90 }
AC=PR {=8cm}
AB=RQ {=3cm}.