ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 8.13). Show that (i) ∆ APB ≅ ∆ CQD (ii) AP = CQ

Question

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 8.13). Show that  (i) ∆ APB ≅ ∆ CQD  (ii) AP = CQ

cdquestions Admin · Accepted Answer

(i) In ∆APB and ∆CQD, ∠APB = CQD (Each 90°) AB = CD (Opposite sides of parallelogram ABCD) ∠ABP = ∠CDQ (Alternate interior angles for AB || CD) ∠∆APB ∠∆CQD (By AAS congruency) (ii) By using the above result ∆APB ∠∆CQD, we obtain AP = CQ (By CPCT)

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 8.13). Show that
(i) ∆ APB ≅ ∆ CQD
(ii) AP = CQ

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions