4. ABC is an isosceles triangle with AB= AC and AD is one of its altitudes (Fig 7.34).

         (i) State the three pairs of equal parts in \bigtriangleup AD\! B and \bigtriangleup ADC.
         (ii) Is \bigtriangleup ADB\cong \bigtriangleup ADC? Why or why not?
         (iii) Is \angle B= \angle C? Why or why not?
         (iv) Is BD= CD? Why or why not?

          

Answers (1)

i) Given in \bigtriangleup AD\! B and \bigtriangleup ADC.

AB= AC

\angle ADB = \angle ADC=90^0

AD = AD   ( Common side) 

 

ii) So, by RHS Rule of congruency, we conclude

\bigtriangleup ADB\cong \bigtriangleup ADC

 

iii) Since both triangles are congruent all the corresponding parts will be equal.

So,

\angle B= \angle C

 

iv) Since both triangles are congruent all the corresponding parts will be equal.

So,

BD= CD.

 

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