Question

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.

(i) seg DE and seg AB

(ii) seg BC and seg AD  

(iii) seg BE and seg AD

Answer 1

The given table is, 

(i) The co-ordinates of points D and E are −7 and 9 respectively.

We know that 9 > −7.

∴ l(DE) = 9 − (−7) = 9 + 7 = 16

The co-ordinates of points A and B are −3 and 5 respectively. We know that 5 > −3.

∴ l(AB) = 5 − (−3) = 5 + 3 = 8

Since, l(DE) ≠ l(AB), so seg DE ≇ seg AB.

(ii) The co-ordinates of points B and C are 5 and 2 respectively.

We know that 5 > 2.

∴ l(BC) = 5 − 2 = 3

The co-ordinates of points A and D are −3 and −7 respectively.

We know that −3 > −7.

∴ l(AD) = −3 − (−7) = −3 + 7 = 4

Since, l(BC) ≠ l(AD), so seg BC ≇ seg AD.

(iii) The co-ordinates of points B and E are 5 and 9 respectively.

We know that 9 > 5.

∴ l(BE) = 9 − 5 = 4

The co-ordinates of points A and D are −3 and −7 respectively.

We know that −3 > −7.

∴ l(AD) = −3 − (−7) = −3 + 7 = 4

Since, l(BE) = l(AD), so seg BE ≅ seg AD.