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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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