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.

Point	A	B	C	D	E
Co-ordinate	$-$3	5	2	$-$7	9

(i) seg DE and seg AB (ii) seg BC and seg AD (iii) seg BE and seg AD

Answer 1

The given table is,

Point	A	B	C	D	E
Co-ordinate	$-$3	5	2	$-$7	9

(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.