Q6 of 23 Page 187

ABCD is a parallelogram AP and CQ are perpendiculars drawn from vertices A and C on diagonal BD (see figure) show that

(i) Δ APB ≅ Δ CQD


(ii) AP = CQ



Given:- ABCD is parallelogram


Formula used :- AAS property


If 2 angles and any one side is are equal in both triangle


Then both triangles are congruent


Solution:-


In Δ APB and Δ CQD


∠ CQD=∠ APB=90°


If ABCD is a parallelogram


∠ CDB=∠ DBA [alternate angles as DC||AB]


AB=DC [opposite sides of parallelogram are equal]


By AAS property


∴ Δ APB ≅ Δ CQD


If Δ APB ≅ Δ CQD


Then


AP=CQ


Conclusion:-


In parallelogram ABCD; Δ APB ≅ Δ CQD


More from this chapter

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4

In the adjacent figure ABCD is a parallelogram P, Q are the midpoints of sides AB and DC respectively. Show that PBCQ is also a parallelogram.


 5

ABC is an isosceles triangle in which AB = AC. AD bisects exterior angle QAC and CD || BA as shown in the figure. Show that

(i) ∠DAC = ∠BCA


(ii) ABCD is a parallelogram



 7

In and DEF, AB || DE, AB=DE; BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see figure). Show that

(i) ABED is a parallelogram


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(iii) AC = DF


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 8

ABCD is a parallelogram. AC and BD are the diagonals intersect at O. P and Q are the points of tri section of the diagonal BD. Prove that CQ || AP and also AC bisects PQ (see figure).