**(1) In ABC and PQR, in a one to one correspondence AB/QR = BC/ PR = CA/ PQ then****(A) PQR ~ ABC(B) PQR ~ CAB(C) CBA ~ PQR(D) BCA ~ PQR**

Given AB/QR = BC/ PR = CA/ PQ

By SSS test of similarity , PQR ~ CAB** .**

Correct option is (B).

**(2) If in DEF and PQR, D Q, R E then which of the following statements is****false?****(A) EF/PR = DF/ PQ****(B) DE/ PQ = EF/ RP****(C) DE/ QR = DF /PQ****(D) EF/ RP = DE/ QR**

**Solution:**

Given D Q, R E

DEF ~QRP…. [AA test of similarity]

DE/QR = EF/RP = DF/QP [Corresponding sides of similar triangles]

DE/ PQ ≠ EF/ RP

Hence option (B) is false.

**(3) In ABC and DEF B = E, F = C and AB = 3DE then which of the statements****regarding the two triangles is true?****(A)The triangles are not congruent and not similar****(B)The triangles are similar but not congruent.****(C)The triangles are congruent and similar.****(D) None of the statements above is true.**

**Solution:**

Given B = E

F = C

ABC ~DEF [AA test of similarity]

Hence option B is the true statement.

**(4) ABC and DEF are equilateral triangles, A (ABC):A(DEF)=1:2****If AB = 4 then what is length of DE?****(A)2√2****(B)4****(C)8****(D)4√2**

**Solution:**

Given A (ABC):A(DEF) = 1:2

ABC and DEF are equilateral triangles.

A = D [Angle equals 60˚]

B = E [Angle equals 60˚]

ABC ~ DEF [AA test of similarity]

A (ABC):A(DEF) = AB^{2}/DE^{2} [Theorem of areas of similar triangles]

1/2 = 4^{2}/DE^{2}

Taking square root on both sides

1/√2 = 4/DE

DE = 4√2

Hence option (D) is the correct answer.

**(5) In figure 1.71, seg XY || seg BC, then which of the following statements is true?****(A) AB / AC = AX / AY****(B) AX / XB = AY / AC****(C) AX / YC = AY / XB****(D) AB / YC = AC / XB**

**Solution:**

Given seg XY || seg BC

AX/BX = AY/YC [Basic proportionality theorem]

(BX/AX ) +1 = (YC/AY) +1

(BX+AX)/AX = (YC+AY)/AY

AB/AX = AC/AY

AB/AC = AX/AY

Hence correct option is (A).