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If in two triangles DEF and PQR, ∠D =∠Q and ∠R = ∠E, then which of the following is not true?
Question

If in two triangles DEF and PQR, ∠D =∠Q and ∠R = ∠E, then which of the following is not true?

A.

EFPR=DFPQ\frac{EF}{PR} = \frac{DF}{PQ} \\​​

B.

DEPQ=EFRP\frac{DE}{PQ} = \frac{EF}{RP} \\​​

C.

DEQR=DFPQ\frac{DE}{QR} = \frac{DF}{PQ} \\​​

D.

EFRP=DEQR\frac{EF}{RP} = \frac{DE}{QR}​​

Correct option is B

Given:
In triangles DEF and PQR,
∠D = ∠Q and ∠E = ∠R
Concept used :
AAA Similarity Criterion – If in two triangles, all three angles are equal, the triangles are similar.
Formula used:
For similar triangles, the ratio of corresponding sides is equal. Based on the correspondence DEFQRP. \triangle DEF \sim \triangle QRP.​​
DEQR=EFRP=DFQP\frac{DE}{QR} = \frac{EF}{RP} = \frac{DF}{QP}​​
Note that  QP is the same side as PQ, and RP  is the same as  PR. So the correct proportionalities are:
DEQR=EFPR=DFPQ\frac{DE}{QR} = \frac{EF}{PR} = \frac{DF}{PQ}​​
Solution:
(A)  EFPR=DFPQ\; \frac{EF}{PR} = \frac{DF}{PQ} This is true as per the correct ratios

(B) DEPQ=EFRP\; \frac{DE}{PQ} = \frac{EF}{RP} This is not true because DE corresponds to QR and PQ corresponds to DF

(C)  DEQR=DFPQ\; \frac{DE}{QR} = \frac{DF}{PQ}​ (This is true as per the correct ratios, since DF/PQ is the same as DF/QP)

(D)   EFRP=DEQR\; \frac{EF}{RP} = \frac{DE}{QR}​ (This is true as per the correct ratios)

The statement that is not true is DEPQ=EFRP. \frac{DE}{PQ} = \frac{EF}{RP}.

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