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F9. 11.307. ABCD is a rectangle (Fig. 11.31) in whichDDP and BQ are perpendiculars from D and Brespectively on diagonal AC. Show that-(i) AADP ACBQ-(i) ZADP CBQ(i) DP-BQA.Fig. 11.31 |
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Answer» (i)In triangle ADP and CBQ,AD = BC (opposite sides of a rectangle are equal)angle DPA = angle BQC(both are right angles)angle DAP = angle BCQ (since AD || BC)Therefore the two triangles are congruent by AAS criterion.(ii) Thus, angle ADP = angle CBQ (by congruent triangles property)(iii) DP = BQ (by congruent triangles property) |
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