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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.

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Solution

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 [BC + CD = BD]

b) AD

AD = AB + BC + CD

= AC + CD [AB + BC = AC]

c) C

Given: AB = BC = CD = DE

AE = AC + CE

So, C is the mid-point of AE.

d) D

Given: AB = BC = CD = DE

CE = CD + DE

So, D is the mid-point of CE.

e) 4

AE = AB + BC + CD + DE

AE = AB + AB + AB + AB [AB = BC = CD = DE]

AE = 4AB


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