Ncert solutions mathematics class 7 Solutions for Chapter 7 congruence of triangles

Exercises in Chapter 7 congruence of triangles Grade 7

Exercise 7.1

Exercise 7.2

Questions in Exercise 7.1

Complete the following statements:

Among two congruent angles, one has a measure of 70° ; the measure of the other angle is ___________.

Q1)

Complete the following statements:

(a) Two line segments are congruent if ___________.

(b) Among two congruent angles, one has a measure of 70°; the measure of

the other angle is ___________.

Give any two real-life examples for congruent shapes.

Q3) If $\triangle ABC\cong\triangle FED$ under the correspondance $ABC\Leftrightarrow FED$ , write all the corresponding congruent parts of the triangle.

If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to

∠E

If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to

∠F

If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to

$\overline{EF}$

Q4) If $\Delta DEF\cong\Delta BCA$ , write the part(s) of $\Delta BCA$ that corresponds to

i) $\angle E$

ii) $\overline{EF}$

iii) $\angle F$

iv) $\overline{DF}$

Questions in Exercise 7.2

Q1) Which congruence criterion do you use in the following?

a) Given: $AC=DF$

$AB=EF$

$BC=EF$

So, $\Delta ABC\cong\Delta DEF$

b) Given: $ZX=RP$

$RQ=ZY$

$\angle PRQ=\angle XZY$

So, $\Delta PQR\cong\Delta XYZ$

c) Given: $\angle MLN=\angle FGH$

$\angle NML=\angle GFH$

$ML=FG$

d) $EB=DB$

$AE=BC$

$\Delta ABE\cong\Delta CDB$

Which congruence criterion do you use in the following?

Given: EB = DB

AE = BC

∠A = ∠C = 90o

So, ΔABE ≅ ΔACD

You want to show that ΔART ≅ ΔPEN,

If you have to use SSS criterion, then you need to show

AR =

Q2) 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) $AT=$

(b) If it is given that

$\angle T=\angle N$ and you are to use SAS criterion,

you need to have

i) $RT=$ and ii) $PN=$

you need to have

i) ?

ii) ?

You want to show that ΔART ≅ ΔPEN,

If it is given that ∠T = ∠N and you are to use SAS criterion, you need to have

RT =

You want to show that ΔART ≅ ΔPEN,

If it is given that AT = PN and you are to use ASA criterion, you need to have

You want to show that ΔART ≅ ΔPEN,

If you have to use SSS criterion, then you need to show

AT =

You want to show that ΔART ≅ ΔPEN,

If you have to use SSS criterion, then you need to show

RT =

Q3) You have to show that $\Delta AMP\cong\Delta AMQ$ In the following proof, supply the missing reasons.

You have to show that ΔAMP ≅ ΔAMQ.

In the following proof, supply the missing reasons.

In ΔABC, ∠A = 30° , ∠B = 40° and ∠C = 110°

In ΔPQR, ∠P = 30° ∠Q = 40° and ∠R = 110°

A student says that ΔABC ≅ ΔPQR by AAA congruence criterion. Is he justified? Why or Why not?

Q4) In $\Delta ABC$ , $\angle A=30\degree$ , $\angle B=40\degree$ and $\angle C=110\degree$

In $\Delta PQR$ , $\angle P=30\degree$ , $\angle Q=40\degree$ and $\angle R=110\degree$

A student says that $\Delta ABC\cong\Delta PQR\$ by AAA

congruence criterion. Is he justified? Why or why not?

Q5) In the figure, the two triangles are congruent. The corresponding parts are marked. We can write $\Delta RAT\cong?$

Q6) Complete the congruence statement:

$\Delta BCA\cong?$

$\Delta QRS\cong?$

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?

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

The triangles are Congruent.

What can you say about their perimeters?

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

The triangles are not Congruent.

What can you say about their Perimeters?

Q8) Draw a rough sketch of two triangles such that they have five pairs of congruent parts but still the triangles are not congruent.

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

Q9) If ∆ABC and ∆PQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?

Explain, why ΔABC ≅ ΔFED

Q10.

Explain, why $\triangle ABC\cong\triangle FED$

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Chapters in this book

Integers

Fractions and Decimals

Data Handling

Simple Equations

Lines and Angles

The Triangle and its properties

Congruence of Triangles

Comparing Quantities

Rational Numbers

Practical Geometry

Perimeter and Area

Algebraic Expressions

Exponents and Powers

Symmetry

Visualising Solid Shapes