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## Answers

Interior angles A and B of triangle ABC are equal,

hence exterior angles CAP and CBQ are equal -----------------(2)

From (1) and (2),

(i) Two sides in triangles ACP and BQC are proportional

(ii) Included angles of these proportional sides are equal

Hence the two triangles are similar.

therefore, AB = AC.

AC²=BQ x AP

ang CAB = ang CBA (angle oppsite to equal sides)

⇒ang CAP = ang CBQ ---------------(1)

In ΔACP and Δ BQC,

also, ang CAB = ang CBA (from (1))

hence,ΔCAP similar to ΔCBQ (SAS)