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# ABC is an isosceles triangle with AB = AC and AD is one of its altitudes (Fig 7.34). State the three pairs of equal parts in bigtriangleup ADB and bigtriangleup ADC. Is bigtriangleup ADB cong bigtriangleup ADC? Why or why not?

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?

Views

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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