Question

Q1. If the diagonals of a parallelogram are equal, then show that it is a rectangle.​

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

■ ANSWER ■

Ref.Image

Ref.Image□ ABCD is a parallelogram

Ref.Image□ ABCD is a parallelogramconsider Δ ACD and Δ ABD

Ref.Image□ ABCD is a parallelogramconsider Δ ACD and Δ ABDAC = BD .... (given)

Ref.Image□ ABCD is a parallelogramconsider Δ ACD and Δ ABDAC = BD .... (given)AB = DC .... (opposite sides of parallelogram)

Ref.Image□ ABCD is a parallelogramconsider Δ ACD and Δ ABDAC = BD .... (given)AB = DC .... (opposite sides of parallelogram)AD = AD .... (common side)

Ref.Image□ ABCD is a parallelogramconsider Δ ACD and Δ ABDAC = BD .... (given)AB = DC .... (opposite sides of parallelogram)AD = AD .... (common side)∴Δ ACD ≅Δ ABD (sss test of congruence)

Ref.Image□ ABCD is a parallelogramconsider Δ ACD and Δ ABDAC = BD .... (given)AB = DC .... (opposite sides of parallelogram)AD = AD .... (common side)∴Δ ACD ≅Δ ABD (sss test of congruence)∠ BAD = ∠ CDA .... (cpct)

Ref.Image□ ABCD is a parallelogramconsider Δ ACD and Δ ABDAC = BD .... (given)AB = DC .... (opposite sides of parallelogram)AD = AD .... (common side)∴Δ ACD ≅Δ ABD (sss test of congruence)∠ BAD = ∠ CDA .... (cpct)∠BAD+∠CDA=180∘. [Adjacent angles of parallelogram are supplementary]

Ref.Image□ ABCD is a parallelogramconsider Δ ACD and Δ ABDAC = BD .... (given)AB = DC .... (opposite sides of parallelogram)AD = AD .... (common side)∴Δ ACD ≅Δ ABD (sss test of congruence)∠ BAD = ∠ CDA .... (cpct)∠BAD+∠CDA=180∘. [Adjacent angles of parallelogram are supplementary]so ∠ BAD and ∠ CDA are right angles as they are congruent and supplementary.

Ref.Image□ ABCD is a parallelogramconsider Δ ACD and Δ ABDAC = BD .... (given)AB = DC .... (opposite sides of parallelogram)AD = AD .... (common side)∴Δ ACD ≅Δ ABD (sss test of congruence)∠ BAD = ∠ CDA .... (cpct)∠BAD+∠CDA=180∘. [Adjacent angles of parallelogram are supplementary]so ∠ BAD and ∠ CDA are right angles as they are congruent and supplementary.Therefor, □ ABCD is a rectangle since a 

Ref.Image□ ABCD is a parallelogramconsider Δ ACD and Δ ABDAC = BD .... (given)AB = DC .... (opposite sides of parallelogram)AD = AD .... (common side)∴Δ ACD ≅Δ ABD (sss test of congruence)∠ BAD = ∠ CDA .... (cpct)∠BAD+∠CDA=180∘. [Adjacent angles of parallelogram are supplementary]so ∠ BAD and ∠ CDA are right angles as they are congruent and supplementary.Therefor, □ ABCD is a rectangle since a parallelogram with one right interior angle is a rectangle.

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