Question

seg DE and segAB are congurent or not?
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Answer 1

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• i. Co-ordinate of the point E is 9

• Co-ordinate of the point D is -7.

• Since, 9 > -7

• ∴ d(D, E) = 9 – (-7) = 9 + 7 = 16

• ∴ l(DE) = 16 …(i)

• Co-ordinate of the point A is -3

• Co-ordinate of the point B is 5.

• Since, 5 > -3

1. ∴ d(A, B) = 5 – (-3) = 5 + 3 = 8

• ∴ l(AB) = 8 …(ii)

• ∴ l(DE) ≠ l(AB) …[From (i) and (ii)]

• ∴ seg DE and seg AB are not congruent.

• ii. Co-ordinate of the point B is 5.

• Co-ordinate of the point C is 2

• Since, 5 > 2

• ∴ d(B, C) = 5 – 2 = 3

• ∴ l(BC) = 3 …(i)

• Co-ordinate of the point A is -3

• Co-ordinate of the point D is -7.

• Since, -3 > -7

• ∴ d(A, D) = -3 – (-7) = -3 + 7 = 4

• ∴ l(AD) = 4 . ..(ii)

• ∴ l(BC) ≠ l(AD) … [From (i) and (ii)]

• ∴ seg BC and seg AD are not congruent.

• iii. Co-ordinate of the point E is 9

• Co-ordinate of the point B is 5.

• Since, 9 > 5

• ∴ d(B, E) = 9 – 5 = 4

• ∴ l(BE) = 4 …(i)

• Co-ordinate of the point A is -3.

• Co-ordinate of the point D is -7.

• Since, -3 > -7

• ∴ d(A, D) = -3 – (-7) = 4

• ∴ l(AD) = 4 …(ii)

• ∴ l(BE) =l(AD) …[From (i) and (ii)]

• ∴ seg BE and seg AD are congruent.

• i.e, seg BE ≅ seg AD

Answer 2

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°°° Solution °°°

Verified by Toppr

Correct option isC

seg BE and seg AD Point A B C D E

Co-ordinates −3 5 2 −7 3

DA=−3−(−7)=4,DC=2−(−7)=3

DB=5−(−7)=12,DE=9−(−7)=3+7=16

AC=2−(−3)=5,AB=5−(−3)=8

AE=3−(−3)=12,

CB=5−2=3,CE=9−2=7

BE=9−5=4

seg DA=BE=4

seg DB=AE=12

Option C seg BE and seg AD