9. In Fig. 6.39, ABC and AMP are two righttriangles, right angled at B

1.	9. In Fig. 6.39, ABC and AMP are two righttriangles, right angled at B and Mrespectively. Prove that:(i) ΔABC-dAMPСА ВСPA MPFig. 6.38 theSoid
Answer» Given:∠ABC = 90° &∠AMP = 90°(i) In ΔABC and ΔAMP, we have ∠A = ∠A (common angle) ∠ABC = ∠AMP = 90° (each 90°) ∴ ΔABC ~ ΔAMP (By AA similarity criterion) (ii) As, ΔABC ~ ΔAMP (By AA similarity criterion) If two triangles are similar then the corresponding sides are equal, Hence, CA/PA = BC/MP

9. In Fig. 6.39, ABC and AMP are two righttriangles, right angled at B and Mrespectively. Prove that:(i) ΔABC-dAMPСА ВСPA MPFig. 6.38 theSoid

Answer»

Given:∠ABC = 90° &∠AMP = 90°(i) In ΔABC and ΔAMP, we have

∠A = ∠A (common angle)

∠ABC = ∠AMP = 90° (each 90°)

∴ ΔABC ~ ΔAMP (By AA similarity criterion)

(ii) As, ΔABC ~ ΔAMP (By AA similarity criterion)

If two triangles are similar then the corresponding sides are equal,

Hence, CA/PA = BC/MP