Home
Class 9
MATHS
ABCD is a parallelogram and AP and CQ a...

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD . Show that
(i) `DeltaA P B~=\ DeltaC Q D`
(ii) `A P\ =\ C Q`

Text Solution

Verified by Experts

`/_APB and /_ CQD`
`angleAPB=90^0=angleCQD=90^0`
AB=CD
`:. angleCDQ=angleQBA`
`anglePAB=angleDCQ`(ASA)
`:./_APB=/_CQD`
`:.AP=CQ`
Promotional Banner

Similar Questions

Explore conceptually related problems

In the given figure, ABCD is a parallelogram in which AN and CP are perpendiculars on diagonal BD. Prove that : (i) DeltaADN =DeltaCBP (ii) AN=CP

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that D P = B Q . Show that: (i) DeltaA P D~= DeltaC Q B (ii) A P = C Q (iii) DeltaA B C (iv) A Q = C P (v) APCQ is a parallelogram.

line l is the bisector of an angle /_A\ a n d/_B is any point on l. BP and BQ are perpendiculars from B to the arms of /_A . Show that: (i) DeltaA P B~=DeltaA Q B (ii) BP = BQ or B is equidistant from the arms of /_A

In a parallelogram ABCD,points P and Q are points of trisection of diagonal BD.Prove that CQ is parallel to AP.

ABCD is a parallelogram with AC and BD as diagonals. Then, A vec C - B vec D =

In Figure, A N and C P are perpendicular to the diagonal B D of a parallelogram A B C Ddot Prove that : A D N~= C B P (ii) A N=C P

In the figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, show that ar( Delta BPC) = ar( Delta DPQ).

ABCD is a parallelogram.bar(AP) bisects /_A and bar(CQ) bisects /_C.P lies on bar(CD) and Q lies on bar(AB0) .Show that