Solution of Chapter 7. Congruence of Triangles (NCERT - Mathematics Book)

Complete the following statements:

(a) Two line segments are congruent if _____.

(b) Among two congruent angles, one has a measure of 70^o; the measure of the other angle is ________.

(c) When we write ∠A = ∠B we actually mean________.

Give any two real-life examples for congruent shapes.

If ∆DEF ∆BCA, write the part(s) of ∆BCA that correspond to:

(i) (ii) (iii) (iv)

Which congruence criterion do you use in the following?

(a) Given: AC=DF

AB=DF

BC=EF

∆ABC ∆DEF

(b) Given: ZX=R

RQ=ZY

∠PQR = ∠XYZ

∆PQR ∆XYZ

(c) ∠MLN = ∠FGH

∠NML = ∠GFH

ML=FG

∆LMN ∆GFH

(d) Given: EB=DB

AE=BC

∠A = ∠C=90^o

∆ABC ∆CDB

You want to show that ∆ART ∆PEN,

(a) If you have to use SSS criterion, then you need to show

(i) AR =

(ii) RT =

(iii) AT =

(iv) AT =

(b) If it is given that ∠T = ∠N and you are to use

SAS criterion, you need to have

(i) RT = and (ii) PN =

(c) If it is given that AT = PN and you are to use

ASA criterion, you need to have

(i) ? (ii) ?

You have to show that . In the following proof, supply the missing reasons.

In ABC, ∠A = 30^o, ∠B = 40^o and ∠C = 110^o. In, ∠P = 30^o, ∠Q = 40^o and ∠R = 110^o. A student says that by AAA congruence criterion. Is he justified? Why or why not?

In the figure, the two triangles are congruent. The corresponding parts are marked. We can write ?

Complete the congruence statement:

?

?

In a squared sheet, draw two triangles of equal areas such that:

(i) The triangles are congruent.

(ii) The triangles are not congruent.

What can you say about their perimeters?

Draw a rough sketch of two triangles such that they have five pairs of congruent parts but still the triangles are not congruent.

If are to be congruent, name one additional pair of corresponding parts. What criterion did you use?

Explain, why