To find the width AB of a river, Sonu walks from A along the bank to C, then the same distance on to D. He then walks at right angles to the bank until B and C are in line, reaching E. Why does DE equal AB?

Question

Accepted Answer

△ABC ≅ △DEC by ASA. ∠BAC = ∠EDC = 90°, AC = DC, and ∠ACB = ∠DCE (vertically opposite). The side AC lies between the two angles, so ASA. By CPCT, DE = AB.

To find the width AB of a river, Sonu walks from A along the bank to C, then the same distance on to D. He then walks at right angles to the bank until B and C are in line, reaching E. Why does DE equal AB?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 9 SAS, ASA and AAS Congruence practice