class 9 NCERT exercise 7.3 question number 4 and 5 math
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4)Given that :
ABC us a triangle
BE and CF are altitudes of sides AC and AB
To prove:
triangle ABE is Congruent to triangle ACF
AB =AC
Proof:
Angle ACF = Angle ABE (each of 90°)
AB = AC (Given)
angleA = angleA (Common)
Therefore, by AAS congruence rule, ∆ABE is congruent to ∆ACF
In ∆ABE congruent to ∆ACF
AB = AC (by CPCT)
5) Given That :
ABC and DBC are isosceles ∆
BC=BC
To prove:
Angle ABD = Angle ACD
Proof:
AB= AC
angle ABC = Angle ACB........1.
BD = CD
angle DBC = angle DCB.......2.
Now,
angle ABC + angle DBC = Angle ACB + angle DCB
= Angle ABD = angle ACD
Hence proved.........
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