Class 7 Maths Chapter 7 Congruence Of Triangle Exercise 7.2 pdf notes:-

**Exercise 7.2** Class 7 maths Chapter 7 Pdf Notes:-

**To see video Solution Of This Exercise Click Here**

## 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

āABC based on bits of information that Appu would give. Tippu attempts to

draw a triangle congruent to āABC, using the information provided by Appu.

The game starts. Carefully observe their conversation and their games.

SSS Game

Appu : One side of āABC is 5.5 cm.

Tippu : With this information, I can draw any number of triangles

but they need not be copies of āABC. 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 āABC.

Appu : Okay. I will give you the length of one more side. Take two sides of āABC 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 āABC. Here are a few

to support my argument:

Appu : Alright. Let me give the lengths of all the three sides. In āABC, 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

also.

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 āABC

Appu : Excellent. So, to draw a copy of a given āABC (i.e., to draw a triangle

congruent to āABC), 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 ā . However, it is common to write it as AB = CD . - Two angles, say, ā ABC and ā PQR, are congruent if their measures are equal. We

write this as ā ABC ā ā PQR or as mā ABC = mā PQR. However, in practice, it is

common to write it as ā ABC = ā 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.