The following table shows points on a number line and their co-ordinat

1.	The following table shows points on a number line and their co-ordinates. Decide whether the pair of segments given below the table are congruent or not.PointABCDECo-ordinate-352-79i. seg DE and seg AB ii. seg BC and seg AD iii. seg BE and seg AD
Answer» 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 ∴ 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

The following table shows points on a number line and their co-ordinates. Decide whether the pair of segments given below the table are congruent or not.PointABCDECo-ordinate-352-79i. seg DE and seg AB ii. seg BC and seg AD iii. seg BE and seg AD

Answer»

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

∴ 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