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Mathematics

In ΔDEF and ΔPQR, it is given that ∠D = ∠Q and ∠R = ∠E, then which of the following is not true?

  1. DEPQ=EFRP\dfrac{DE}{PQ} = \dfrac{EF}{RP}

  2. DEQR=DFPQ\dfrac{DE}{QR} = \dfrac{DF}{PQ}

  3. EFPR=DFPQ\dfrac{EF}{PR} = \dfrac{DF}{PQ}

  4. EFRP=DEQR\dfrac{EF}{RP} = \dfrac{DE}{QR}

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Answer

Given, in ΔDEF and ΔPQR:

∠D = ∠Q

∠E = ∠R

∴ ΔDEF ∼ ΔQRP by AA similarity.

The ratio of corresponding sides is:

DEQR=DFQP\dfrac{DE}{QR} = \dfrac{DF}{QP}

DEPQ=EFRP\dfrac{DE}{PQ} = \dfrac{EF}{RP} do not hold true.

Hence, option 1 is the correct option.

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