PQR is a triangle, S is a point on the side QR of ΔPQR such that ∠PSR = ∠QPR. Given QP = 8 cm, PR = 6 cm and SR = 3 cm. (i) Prove ΔPQR ΔSPR. (ii) Find the length of QR and PS. (iii) Find .

Question

KnowledgeBoat · Accepted Answer

(i) In ΔPQR and ΔSPR, ⇒ ∠PSR = ∠QPR [Given ] ⇒ ∠PRQ = ∠PRS [Common angle] ΔPQR ΔSPR by AA similarity. Hence, proved that ΔPQR ΔSPR. (ii) Since, ΔPQR ΔSPR and corresponding sides of similar triangle are proportional to each other. Also, Hence, QR = 12 cm and PS = 4 cm. (iii) We know that, Ratio of areas of two similar triangles is same as the square of the ratio between their corresponding sides. Hence,

Mathematics

PQR is a triangle, S is a point on the side QR of ΔPQR such that ∠PSR = ∠QPR. Given QP = 8 cm, PR = 6 cm and SR = 3 cm. (i) Prove ΔPQR ΔSPR. (ii) Find the length of QR and PS. (iii) Find .

Similarity

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Mathematics

PQR is a triangle, S is a point on the side QR of ΔPQR such that ∠PSR = ∠QPR. Given QP = 8 cm, PR = 6 cm and SR = 3 cm. (i) Prove ΔPQR ΔSPR. (ii) Find the length of QR and PS. (iii) Find .

Similarity

Related Questions

In ΔABC, D and E are mid-points of AB and AC respectively.Find: ar(ΔADE) : ar(ΔABC).

If ΔABC and ΔDEF are similar triangles in which ∠A = 47° and ∠E = 83°, then ∠C equals :50°60°70°80°

In ΔABC, D and E are mid-points of AB and AC respectively.
Find: ar(ΔADE) : ar(ΔABC).

If ΔABC and ΔDEF are similar triangles in which ∠A = 47° and ∠E = 83°, then ∠C equals :
50°
60°
70°
80°