Question

Question 21

Fill in the blanks to make the statements true.
In the given figure, points A, B, C, D and E are collinear, such that AB = BC = CD = DE. Then,

a) AD = AB + _________

b) AD = AC + _________
c) Mid-point of AE is ______
d) Mid-point of CE is ______
e) AE = ______ AB.

Answer 1

Three or more points are said to be collinear if they lie on a single straight line.

a) AD

AD = AB + BC + CD

= AB + BD $[\because BC+CD=BD]$

b) AD

AD = AB + BC + CD

= AC + CD $[\because AB+BC=AC]$

c) C

Given: AB = BC = CD = DE

$\therefore AE=AC+CE$

So, C is the mid-point of AE.

d) D

Given: AB = BC = CD = DE

$\therefore CE=CD+DE$

So, D is the mid-point of CE.

e) 4

AE = AB + BC + CD + DE

AE = AB + AB + AB + AB $[\because AB=BC=CD=DE]$

$\therefore$ AE = 4AB