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# Fill in the blanks so that the following statements are true:

The correspondence ABC ↔ PQR is a similarity in Δ ABC and ΔPQR. AB = 16, AC = 8, PQ = 24, BC = 12, then QR + PR = ____.

Answer :

Given: The correspondence ABC ↔ PQR is a similarity in ∆ABC and ∆PQR.

AB = 16,

AC = 8,

PQ = 24 &

BC = 12

To find: QR + PR = ?

By definition, for a given correspondence between the vertices of two triangles, if the corresponding angles of the triangles are congruent and the lengths of the corresponding sides are in proportion, then the given correspondence is a similarity between two triangles.

⇒

⇒

⇒

To find (QR + PR), cross multiply it.

⇒ (QR + PR) × AB = (BC + AC) × PQ

Substituting values,

⇒ (QR + PR) × 16 = (12 + 8) × 24

⇒ (QR + PR) × 16 = 20 × 24

⇒

⇒ QR + PR = 30

**Thus, the answer is 30.**

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