Page 6 - ln1

Solution:
Consider point S on the line BC so that BD = SD and join AS.

Consider △ ADB and △ ADS
We know that SD = BD
Since AD is a perpendicular we know that
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∠ ADB = ∠ ADS = 90
AD is common i.e. AD = AD
By SAS congruence criterion
△ ADB ≅△ ADS
AB = AS (c. p. c. t)
Consider △ ABS
We know that AB = AS
From the figure we know that ∠ ASB and ∠ ABS are angles opposite to the equal sides
∠ ASB = ∠ ABS …. (1)
Consider △ ACS
From the figure we know that ∠ ASB and ∠ ACS are angles opposite to the equal sides
∠ ASB = ∠ ACS …. (2)
Considering the equations (1) and (2)
∠ ABS >∠ ACS
It can be written as∠ ABC >∠ ACB
So we getAC > AB
Therefore, it is proved that AC > AB.

Question 4.
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In △ABC, side AB is produced to D such that BD = BC. If ∠A = 70 and ∠B = 60 ,
prove that
(i) AD > CD
(ii) AD > AC.

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In △ ABC it is given that ∠ A = 70 and ∠ B = 60
Based on the sum property of the triangle
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∠ A + ∠ B + ∠ C = 180
To find ∠ C