Class 7 Maths Chapter 7 Congruence Of Triangle Exercise 7.2 pdf notes:-
Exercise 7.2 Class 7 maths Chapter 7 Pdf Notes:-
Ncert Solution for Class 7 Maths Chapter 7 Congruence Of Triangle Exercise 7.2 Tips:
CRITERIA FOR CONGRUENCE OF TRIANGLES
We make use of triangular structures and patterns frequently in day-to-day life. So, it is
rewarding to find out when two triangular shapes will be congruent. If you have two triangles
drawn in your notebook and want to verify if they are congruent, you cannot everytime cut
out one of them and use method of superposition. Instead, if we can judge congruency in
terms of approrpriate measures, it would be quite useful. Let us try to do this.
A Game Appu and Tippu play a game. Appu has drawn a triangle ABC and
has noted the length of each of its sides and measure of each of its angles.
Tippu has not seen it. Appu challenges Tippu if he can draw a copy of his
∆ABC based on bits of information that Appu would give. Tippu attempts to
draw a triangle congruent to ∆ABC, using the information provided by Appu.
The game starts. Carefully observe their conversation and their games.
Appu : One side of ∆ABC is 5.5 cm.
Tippu : With this information, I can draw any number of triangles
but they need not be copies of ∆ABC. The triangle I draw may beobtuse-angled or right-angled or acute-angled. For example, here are a few.I have used some arbitrary lengths for other sides. This gives me many triangles with
length of base 5.5 cm.
So, giving only one side-length will not help me to produce a copy of ∆ABC.
Appu : Okay. I will give you the length of one more side. Take two sides of ∆ABC to be
of lengths 5.5 cm and 3.4 cm.
Tippu : Even this will not be sufficient for the purpose. I can draw several triangles
with the given information which may not be copies of ∆ABC. Here are a few
to support my argument:
Appu : Alright. Let me give the lengths of all the three sides. In ∆ABC, I have AB = 5cm,
BC = 5.5 cm and AC = 3.4 cm.
Tippu : I think it should be possible. Let me try now.
First I draw a rough figure so that I can remember the lengths easily.
I draw BC with length 5.5 cm.
With B as centre, I draw an arc of radius 5 cm. The point A has to be somewhere on
this arc. With C as centre, I draw an arc of radius 3.4 cm. The point A has to be on this arc
So, A lies on both the arcs drawn. This means A is the point of intersection of the arcs.
I know now the positions of points A, B and C. Aha! I can join them and get ∆ABC
Appu : Excellent. So, to draw a copy of a given ∆ABC (i.e., to draw a triangle
congruent to ∆ABC), we need the lengths of three sides. Shall we call this condition
as side-side-side criterion
Tippu : Why not we call it SSS criterion, to be short?
SSS Congruence criterion:
If under a given correspondence, the three sides of one triangle are equal to the three
corresponding sides of another triangle, then the triangles are congruent.
WHAT HAVE WE DISCUSSED?
- Congruent objects are exact copies of one another.
- The method of superposition examines the congruence of plane figures.
- Two line segments, say, AB and CD , are congruent if they have equal lengths. We
write this as AB CD ≅ . However, it is common to write it as AB = CD .
- Two angles, say, ∠ABC and ∠PQR, are congruent if their measures are equal. We
write this as ∠ABC ≅ ∠PQR or as m∠ABC = m∠PQR. However, in practice, it is
common to write it as ∠ABC = ∠PQR.
- SSS Congruence of two triangles:
Under a given correspondence, two triangles are congruent if the three sides of the
one are equal to the three corresponding sides of the other.
- SAS Congruence of two triangles:
Under a given correspondence, two triangles are congruent if two sides and the angle
included between them in one of the triangles are equal to the corresponding sides and
the angle included between them of the other triangle.