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# 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 ∠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)?

**Solution:**

(a) Two triangles are said to be congruent by SSS criterion if and only if, all the three sides of one triangle are equal to all the three sides of another triangle.

Hence, if ∆ ART ≅ ∆ PEN by SSS criterion, then

(i) AR = PE

(ii) RT = EN and

(iii) AT = PN.

(b) Two triangles are said to be congruent by SAS criterion if and only if two sides and angle between them of one triangle are equal to the two sides and angle between them of another triangle.

Hence. if ∆ ART ≅ ∆ PEN by SAS criterion, and if it is given that ∠T = ∠N by SAS criterion, then

(i) RT = EN

(ii) PN = AT

(c) Two triangles are said to be congruent by ASA criterion if and only if two angles and sides between them of one triangle are equal to the two angles and sides between them of another triangle.

Hence, if ∆ ART ≅ ∆ PEN by ASA criterion, and if it is given that AT = PN by ASA criterion, then

(i) ∠T = ∠N.

(ii) ∠A = ∠P

**☛ Check: **NCERT Solutions for Class 7 Maths Chapter 7

**Video Solution:**

## 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 =

NCERT Solutions for Class 7 Maths Chapter 7 Exercise 7.2 Question 2

**Summary:**

We want to show that ∆ART ≅ ∆PEN, (a) If we have to use SSS criterion, then we need to show i) AR = PE, ii) RT = EN and, iii) AT = PN (b) If it is given that ∠T = ∠N and we are to use SAS criterion, we need to have i) RT = EN ii) PN = AT and (c) If it is given that AT = PN and we are to use ASA criterion, we need to have i) ∠T = ∠N ii) ∠A = ∠P

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