In figure, ABCD and AEFD are two parallelograms. Prove that ar (APEA) = ar(AQFO). -Maths 9th

In figure, ABCD and AEFD are two parallelograms. Prove that ar (APEA) = ar(AQFO). -Maths 9th
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Given, ABCD and AEFD are two parallelograms. To prove ar (APEA) = ar (AQFD) Proof In quadrilateral PQDA, AP || DQ [since, in parallelogram ABCD, AB || CD ] and PQ || AD [since, in parallelogram AEFD, FE || AD] Then, quadrilateral PQDA is a parallelogram. Also, parallelogram PQDA and AEFD are on the same base AD and between the same parallels AD and EQ. ar (parallelogram PQDA) = ar (parallelogram AEFD) On subtracting ar (quadrilateral APFD) from both sides, we get ar (parallelogram PQDA)- ar (quadrilateral APFD) = ar (parallelogram AEFD) – ar (quadrilateral APFD) ⇒ ar (AQFD) = ar (APEA) Hence proved.
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Related questions

In figure, ABCD and AEFD are two parallelograms. Prove that ar (APEA) = ar(AQFO). -Maths 9th

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Last Answer : Given, ABCD and AEFD are two parallelograms. To prove ar (APEA) = ar (AQFD) Proof In quadrilateral PQDA, AP || DQ [since, in parallelogram ABCD, AB || CD ] and PQ || AD [since, in parallelogram AEFD ... APFD) = ar (parallelogram AEFD) - ar (quadrilateral APFD) ⇒ ar (AQFD) = ar (APEA) Hence proved.

In the adjoining figure, ABCD is a parallelogram in which AB is produced to E so that BE = AB. Prove that ED bisects BC -Maths 9th

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Last Answer : Given, ABCD is a parallelogram. BE = AB To show, ED bisects BC Proof: AB = BE (Given) AB = CD (Opposite sides of ||gm) ∴ BE = CD Let DE intersect BC at F. Now, In ΔCDO and ΔBEO, ∠DCO = ... CD (Proved) ΔCDO ≅ ΔBEO by AAS congruence condition. Thus, BF = FC (by CPCT) Therefore, ED bisects BC. Proved

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Last Answer : In △PAD, ∠A = 90° and DA = PA = PB ⇒ ∠ADP = ∠APD = 90° / 2 = 45° Similarly, in △QBC, ∠B = 90° and BQ = BC = AB ⇒∠BCQ = ∠BQC = 90° / 2 = 45° In △PAD and △QBC , we have PA = QB [given] ∠A = ... [each = 90° + 45° = 135°] ⇒ △PDC = △QCD [by SAS congruence rule] ⇒ PC = QD or DQ = CP

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Last Answer : We know that opposite angles of a paralleloram are equal . ∴ ∠P = ∠R ⇒ 3x - 4 = 56 - 3x ⇒ 6x = 60 ⇒ x = 10 Thus, ∠P = ∠R = 3 10 - 4 = 26° Also, ∠P + ∠Q = 180° [ ... Hence, the four angles of the parallelogram PQRS are 26°, 154°,26° and 154°. We should care our earth to have good eco balance.

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Last Answer : Join PR. ∵ △PSR and ||gm APRD are on the same base and between same parallel lines. ar(△PSR) = 1/2 ar(||gm APRD) Similarly, ar(△PQR) = 1/2 ar(||gm PBCR) ar(△PQRS) = ar(△PSR) + △(PQR) = 1/2 ar(||gm APRD) + 1 ... |gm PBCR) = 1/2 ar(||gm ABCD) ⇒ ar(||gm ABCD) = 2 ar(||gm PQRS) = 2 32.5 = 65cm2

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