Q. 64.3( 21 Votes )

# 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

Answer :

__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

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PREVIOUSABC 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 parallelogramNEXTIn 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(ii) BCFE is a parallelogram(iii) AC = DF(iv) ∆ABC ≅ ∆DEF

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